ORDER DEGREE LINEAR OR NON- LINEAR a2u a?u a2u = 0 ax2 ay2 ' az² (x + y)dx + (3x? – 1)dy = 0 d²r d?r 3 + dr +yT

Q: 1. y(x + 1)dx - (x² – 5x + 6)dy = 0; x = 4 where y = 1 = 3xy2; x = 2 where y = -2 %3D dx 2. dy

A: dxdy=3xy2 ; x=2 where y=-2

Q: (4D4-24D³ +35D² +6D-9)y = 0

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Q: a) 2+ + = 1. H

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: 10. хx" + 4xx'%3D у2

A:

Q: 1. x' + y'-y = 2et + 1; x(0) = 2, x'(0) = 3, y(0) = 3 2x" - y' = et

A: Our objective is given below:According to our guidelines we can solve only the first question if…

Q: dy +y cot x = cos .x dx dy = xe* – 3y dx dy 1 = 2 x+1 -y |y(1) =1 dx

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Q: c.) 3x²y"-6xy³y' + 4x = 0 d.) 3xd³y_d²y dx³ dx² -5xy = 3x²y

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Q: х' %3D —х +у— 8 y = y' = 3x + y – 4t

A: We need to find the solution to the following system of differential equations.…

Q: (D² + 3D - 10)y = 0; when y(0) = 0

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Q: 7. (4Dª – 4D³ – 23D2 + 12D + 36)y =0 8. (18D3 – 33D² + 20D – 4)y = 0

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Q: а. (x? + у?)dx + 2хydy%3D0 a2u a?u b. Əx2 a2u = 0 yy" = x

A: According to our guidelines , we can answer only first three sub-parts. Kindly re-post other…

Q: 2xydx – V x² + y²dy = 0

A: The solution is given as

Q: 47x +75y -30x - 48y satisfying the initial conditions r(0) = 19 and ly' y(0) 12. x(t) = y(t) =

A: Given equations  are  x'=47x+75yy'=-30x-48y  with the initial conditions x0=19 and y0=-12 To find…

Q: 7. L+ Ri = E,where L, R, and E are constants when t = 0, i = 0 t%3D dt

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Q: 5. (D²2D+1)y=e* arctan x

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Q: Find the general solution of the following system of differential equation.

A: We will find out the required solution.

Q: dy b) x= 2y+3x dx dy d) x+y=2.r, y(2)=1 dx dy f) x+y=e* dx

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Q: 2. (x² + y²)dx +x²dy = 0 %3D

A: The solution is given as