Differential Equations Answers

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

 𝑥2𝑦=1+𝑐𝑥

𝑦𝑠𝑖𝑛(𝑥) − 𝑥𝑦2 = 𝑐

Suppose it is known that the population of the community in problem 1 is 10000 after 3 years.