(b) y" +y + y³ = 0

Q: Z4 =:₂₁ (4x²yz - dz dy dx S₁

A: Given ∫23∫-14∫104x2yz-z44dz dy dx ∫23∫-14∫104x2yz-z44dz dy dx=∫23∫-14∫104x2yz dz dy dx -…

Q: 2 V4-22 xy dy dx dz

A:

Q: 3 9 dx dt -1 -3 with x(0) : 4 Give your solution in real form. X1 = X2 = 2. II

A: The objective is to solve the differential equation:

Q: Find the general solution of (x+2y– 4)dx-(2x+5-y)dy=0

A: The given differential equation is of Reducible Homogeneous form . We solve it using following way .

Q: Find the particular solution of csc y dx + sec2 x dy = 0; y = π/2 when x = π/2

A: We solve this differential equation by separation of variables.

Q: 1 В(т, п) ym-1(a – y)"-'dy. am+n-1

A:

Q: 10.(x + Jy² + 1)dx – (y-- -(y- |dy = 0. y2+1

A:

Q: (교2 + y2 - 5)dz = (y + zy)dy,

A:

Q: Obtain the particular solution when x = 1 and y = 1 3 y°) dx 3 - x(x + y) dy = 0

A:

Q: 6x + y²) dx + y(2x – 3y) dy = 0 -

A: Exact differencal equation and second eliminate contact

Q: 5. (1+2xVx2 - y² )dx-(2yVx2-y? )dy =0

A:

Q: 2.) 2 (x -y)dx + (3x² - GxY - 2x) dy

A:

Q: 6. (2z – 1)(y – 1)dr + (x+ 2)(x – 3)dy = 0, y(1) = -1

A:

Q: (x²-xy-y²\ (x2-ху-у?) dy = 0 dx + r2-v3

A:

Q: б бу-гу2 -14-292 y dx dy

A:

Q: 4. (x+ 2y-1)dx-(2x+y-5) dy =o

A: According to question,Given differential equation,x+2y-1dx-2x+y-5dy = 0

Q: _x- y-1dx+(4y +x-1)dy = 0; y(2)=1

A:

Q: 2r-r2 -3 zVx2 + y2 dz dy dx. 0. 0.

A:

Q: 2²ye+v°-²dx dy dz 1 -1

A: We have to calculate the integral.

Q: -2dх 38. y-2dx dy er e2x + 1' УО) %3D 1

A:

Q: -4x-2 FInd given y =-2 dx Sx+3

A: By using partial differentiation.

Q: dy y dx 2x = 3y2 – 2 when y = 1 and x = 1 in terms of x. %3D - -

A:

Q: [2x*yžcosx² – 2x*yå + x/5]dx + [x/5stnx² - x° /9]dy = 0 3 2x²yz + x [x/ysinx? – x³ /y]dy = 0 -

A:

Q: Determine the general solution of (x-2y)dx + (2x+y)dy = 0

A: See the details solution in below

Q: The general solution of (y-1)dx −2(x+y+1)dy=0 by CL2V is

A:

Q: 3. Find the General and Particular solution of = 3y ; y= 3,when x = 0 dx

A: Take integration on both side and then put initial value

Q: 4- S" e-x* dx 5- Vy e-y² dy

A:

Q: Find the general solution of 6y2 dx - x (2x3 + y) dy = 0

A:

Q: 12-y² y !! dz dx dy 2. 0 0

A: triple intregal

Q: dy e2x -3 Find if y = In %3D dx 1-4x

A: SOLUTION-

Q: 22 32 S[ (4-y ) dydx 1. ans:- 3 0 0

A:

Q: Find the general solution of (x+2y– 4)dx-(2x+5-y)dy = 0

A:

Q: 4e-2t 6] d - x(0)= 1; y(0)=1 dt 1 8t x(1)=?

A: From the given matrix equations, we get:Given:A=-1210b(t)= 4e-2t-6 8t x0=1; y0=1To find: x1=?

Q: + 4 oly +6y =0 dt dy +2 -6x=6

A: Introduction:Simultaneous equations are those in which the derivatives of two or more dependent…

Q: 1- (2 xy-4 y) dx+(3x²y-8x) dy30

A:

Q: Evaluate the integrals

A: Consider the given integral, ∫02∫-4-y24-y2∫02x+ydz dx dy integrate with the given order of the…

Q: Vy2 -25 dy S y3

A:

Q: 2y4 y3 – y2 + y – 1 dy = y² + 2y + In ly – 1| -in ly2 + 1| - y +C

A:

Q: 1 y2e- dy 7 صواب ihi

A:

Q: 1-x²-y² /1-x2-y2 1-х2 (x² + y²)dz dy dx -/1-x2

A:

Q: 3- dy + 3x^²y = x³6 s dx Y- XLnx dy dy +y = ₂l₁x dx 2Lnx ets

A:

Q: Find the particular solution of csc y dx + sec² x dy = 0; y = when x = 2 2

A: Given differential equation is cscy dx+sec2x dy=0. To find the particular solution if y=π2 when…

Q: (3x -y - 4) dy t (x+y-4) dx = 0, 2. 14

A:

Q: 2x[3x +y- y exp(-x²)]dx + [x² + 3y² + exp(-x²)]dy = 0 IC:X = 0, y = 1

A:

Q: -3 -2 ²₁ ² [z³(x + y)³] dz dy dx

A:

Q: .x(3xy-4y3 + 6)dx + (x³ - 6x²y2 - 1)dy = 0, when x = 2, y = 0

A:

Q: 1 dz -÷z³ = t² + 3t – 2 dt 3 z2 -

A: Differential equations and their type