Differential Equations Answers

Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation.

x dy/dx + y = 1/y^2

d^y/dx^-4y=xsinhx

solve 8y''-2y'-y=x²+x+1

Find the integral surface of the equation 4yzp+q+2y=0 passing through

y²+z²=2,x+z=1

Solve [(D³+D²D¹-D(D¹)^2-(D¹)^3]z = e^xcos2y

Use linear substitution to solve the following first-order differential equation

𝑑𝑦/𝑑𝑥=(2𝑥+𝑦)/(2𝑥+𝑦+1)

A tank contains 200 liters of fresh water .Brine containing 2.5 N/liter of dissolved salt runs into the tank at the rate of 8 liters/min and the mixture kept uniform by stirring runs out at 4 liters per minute .Find the amount when the tank contains 240 liters of brine. The concentration of the salt in the tank after 25 minutes amounts to how much

Obtain the particular solution

1. dy/dx+2y=y^3e^4x, y(0)=1. ans. y^2 (1-2x)=e^-4x

2.dy/dx - y/x=y^5/x^3 ,y(1)=-1. ans. y^4(3-2x^2)=x^4

Solve the initial value problem

y"-5y'+6y=2e^x, y(0)=1, y'(0)=1.

𝑢(x,0); { 60𝑥, 0 < 𝑥 < 1, 60(2-𝑥), 1 ≤ 𝑥 < 2