Find the general solution to the 2nd order ODE: y" + 4y' + 4y = √xe -2x

Q: 7. y - y = 16

A: The objective is to find the general solution .

Q: 5) Solve the Non-linear second ODE: d²y + 3 x² y dx? y? = x² ) (dy %3D

A: Given: Non-linear second order differential equation is 3 x2 y d2ydx2+y2=x2(dydx)2

Q: Construct an equation whose roots are the reciprocal of the roots of 2x +4x -10x-5=0

A: Consider a cubic equation ax3+bx2+cx+d=0 where a≠0 and assuming α,β and γ are roots of equation then…

Q: 1 + e1x+10 + 4" +x – 5) dx + xA 4x-

A:

Q: calculate y" and y"'. y = 7 − 2x

A: Given function: y=7-2x

Q: Evaluate (3x + cos 4x) dx

A:

Q: 2. [x² √x + 1 dx

A:

Q: Find mZX (3y-71° X Y (2x) O W (x+181° (3y + 1)º

A: Solve for the angle X

Q: Solve the First ODE (3y* – x*)dx = 3xy'dy || 4-4ln(2x)+c А-у %3D 4 4-4ln(x)+c B- y = 2 4-4ln(x)+c C-…

A:

Q: Eliminate the arbitrary constant. y=Ax 5 + Bx3

A:

Q: Find when y = -5 (In(x))¯4

A: Explanation of the answer is as follows

Q: (cosh ar +h)dr

A:

Q: O ex+e-x

A:

Q: Compute 3+r+1 dx x2

A: Given : ∫233x2+2x+1x2dx

Q: Find the general solution of the given ODE x+1 v +1

A: dydx=x+1y4+1 (y4+1)dy=(x+1)dx Integrate both sides ∫(y4+1)dy=∫(x+1)dx∫y4 dy + ∫dy  = ∫x dx + ∫dxy55…

Q: Find the solution of the following linear ODE given that y(5)=3 dy Зу = (x – 4)² х—4 dx

A: Use integrating factor for the differential equation.

Q: 2х — 3 /3x2 — 9х + 27

A: Consider an integral of the form, The integral of this form can be solved using the substitution…

Q: Evaluate х2 + 2х — 1 х3 — х

A:

Q: Find y" given 3xy³ + 2xy = 5

A:

Q: 11x+8 1. S x²+x-6 dx

A: