# IIT JAM Mathematics Test Series 2023 : Differential Equations – Method of Variation of Parameters

Practice IIT JAM Mathematics Test Series for Free only On www.examflame.com and make your concepts more crystal and clear. In the Series of Tests for IIT JAM 2023, you will get topic-wise Tests. IIT JAM Mathematics Test Series 2023 : Differential Equations – Method of Variation of Parameters . These Questions are prepared as per the Latest Syllabus of IIT JAM Mathematics 2023 . Practicing mock tests/Test series, you will get an idea about how and which type of Question will ask in the Examination. It also boost your confidence and enhance your preparation level. Also Solve IIT JAM Mathematics Previous Year Question Paper. And Don’t Forget to Share with Your Friends.

## IIT JAM Mathematics Test Series 2023 : Differential Equations – Method of Variation of Parameters

Q1. Apply the method of variation of parameters to solve

y2 + a2y = cosec ax

• (a) y = C1 cos ax + C2 sin ax – (x/a) × cos ax + (1/a2) × cos ax log sin ax
• (b) y = C1 sin ax + C2 cos ax – (x/a) × cos ax + (1/a2) × sin ax log sin ax
• (c) y = C1 cos ax + C2 sin ax – (x/a) × cos ax + (1/a2) × cos ax log cos ax
• (d) y = C1 cos ax + C2 sin ax – (x/a) × sin ax + (1/a2) × sin ax log cos ax

Q2. Apply the method of variation of parameters to solve

y2 – 4y1 + 3y = ex/(1 + ex)

• (a) y = C1 e-x + C2 e3x + (1/2) × (ex– e3x) log (1 – e–x) + (1/2) × e2x
• (b) y = C1 ex + C2 e3x + (1/2) × (ex– e3x) log (1 + e–x) + (1/2) × e2x
• (c) y = C1 ex + C2 e3x + (1/2) × (ex– e3x) log (1 – e–x) + (1/2) × e-2x
• (d) y = C1 e-x + C2 e3x + (1/2) × (ex– e3x) log (1 + e–x) + (1/2) × e2x

Q3. Using method of variation of parameters, solve

d2y/dx2 – 2(dy/dx) + y = x ex sin x

with y (0) = 0 and (dy/dx)x=0 = 0.

• (a) y = ex (2 – x sin x – 2 cos x).
• (b) y = ex (2 + x sin x – 2 sin x).
• (c) y = ex (2 – x sin x – 2 cos x).
• (d) y = ex (2 + x cos x – 2 cos x).

Q4. Apply the method of variation of parameters to solve

x2y2 + xy1 – y = x2ex

• (a) y = C1 x + C2 x–1 + ex (1 + x–1)
• (b) y = C1 – C2 x–1 – ex (1 – x–1)
• (c) y = C1 x + C2 – ex (1 + x–1)
• (d) y = C1 x + C2 x–1 + ex (1 – x–1)

Q5. Apply the method of variation of parameters to solve

x2 y” – 2xy’ + 2y = x log x, x > 0

• (a) y = C1x + C2x2 – (x/2) × (log x)2 – x (1 + log x)
• (b) y = C1x + C2x2 – (x/2) × (log x) + x (1 + log x)
• (c) y = C1x – C2x2 + (x/2) × (log x) + x (1 + log x)
• (d) y = C1x + C2x – (x/2) × (log x)2 – x (1 – log x)

Q6. Solve

y2 – 2y1 + y = x ex log x, x > 0

by the method of variation of parameters.

• (a) y = C1 e + C2 x ex – (1/6) × x3 ex log x – (5/36) × x3 ex
• (b) y = C1 ex + C2 x ex + (1/6) × x3 ex log x – (5/36) × x3 ex
• (c) y = C1 e + C2 x ex + (1/6) × x ex log x + (5/36) × x3 ex
• (d) y = C1 ex + C2 x ex + (1/6) × x ex log x + (5/36) × x3 ex

Q7. Solve the differential equation

(D2– 2D + 2) y = ex tan x

by method of variation of parameters

• (a) y = ex (C1 cos x – C2 sin x) + ex cos x log (sin x – tan x)
• (b) y = ex (C1 cos x – C2 sin x) – ex cos x log (sin x – tan x)
• (c) y = ex (C1 cos x + C2 sin x) – ex cos x log (sin x + tan x)
• (d) y = ex (C1 cos x – C2 sin x) – ex cos x log (sin x + tan x)

Q8. Apply the method of variation of parameters to solve

y3 – 6y2 + 11y1 – 6y = e2x

• (a) y = c1ex – c2e2x + c3e3x+ x e2x
• (b) y = c1ex + c2ex – c3e3x– x e2x
• (c) y = c1ex – c2e2x + c3ex– x e2x
• (d) y = c1ex + c2e2x – c3e3x– x e2x

Q9. Find the particular integral of

(d2y/dx2) – 2(dy/dx) + y = 2x

by the method of variation of parameters

• (a) 2x + 4
• (b) 4x + 2
• (c) 2x – 4
• (d) 4x – 2

Q10. Apply the method of variation of parameters to solve

d2y/dx2 + y = sec3 x

• (a) y = c1 sin x – c2 sin x + sin tan x
• (b) y = c1 cos x + c2 sin x + (1/ 2) sin tan x
• (c) y = c1 sin x – c2 sin x + (1/ 2) sin tan x
• (d) y = c1 cos x + c2 sin x – (1/ 2) tan sinx

Hope you like the test given above for IIT JAM Mathematics 2023 of  Topic – Method of Variation of Parameters of the Chapter Differential Equations . To get more Information about any exam, Previous Question Papers , Study Material, Book PDF, Notes etc for free, do share the post with your friends and Follow and Join us on other Platforms links are given below to get more interesting information, materials like this.

### Important Searches & Tags

• IIT JAM Mock Test Papers download
• IIT JAM test series
• Free Mock Test mathematics Mock Test
• IIT JAM Test series mathematics
• Eduncle IIT JAM Test Series
• Free Mock Test for IIT JAM Mathematics
• IIT JAM Mathematics Mock Test 2022
• IIT JAM Mock Test
• IIT JAM free Mock Test 2022
• IIT JAM Mathematics topic wise questions PDF
• IIT JAM 2022 mock Test
• Best Test Series for IIT JAM Mathematics
• Free Online Test Series for IIT JAM Mathematics
• IIT JAM mock Test 2022
• IIT JAM free Mock Test 2022
• Unacademy IIT JAM Mathematics test series
• DIPS academy Test series
• Career Endeavour Test Series IIT-JAM
• Career Endeavour Test Series pdf

close