5. The variables x and y are related by the following differential equation. dy x+y = dr x-y By using the substitution y = vx, show that the differential equation can be written a du 1+v² dr Hence or otherwise, find the general solution of the differential equation. x

Q: Give a general solution formula for the differential equation da2 + 49y 0. Use a and b for the…

A: given d2ydx2+49y=0 auxiliary equation  m2+49=0⇒ m=±-49⇒ m=±7i hence general solution…

Q: Use the method for solving Bernoulli equations to solve the following differential equation. dy y dx…

A: Consider: dydx+yx-10=5x-10y12⇒1y12dydx+y12x-10=5x-10                         ...(1) Let y12=t. So,…

Q: Solve for General/Particular Solution for the following differential equations. 2xe2Ydy + (e²y –…

A: First let's check the given D.E. is exact or not.

Q: 4 dz = (4x²y + x²)dx + (²x³ — y²)dy = 0

A:

Q: Use the method for solving Bernoulli equations to solve the following differential equation. 1 3 dy…

A: We solve given  Bernoulli's equation.

Q: Determine whether the given function is a solution of the differential equation. y = √√√x; xy' - y =…

A: Given a differential equation xy'-y=0. To determine whether function y=x is a solution of the…