Differential Equations Answers

Use taylors series method to find approximate Value of y at x =0.2,given that dy/dx =2y+3ex,y(0)=0 comapre the result by solving the differential equation

(D² − 3DD + 2D²)z = e²x+³y +sin(x-2y)

1.       Solve the exact differential equation (𝗑 − 2𝑒^𝑦)𝑑𝑦 + (𝑦 + 𝗑 sin 𝗑)𝑑𝗑 = 0.

2.     Solve the differential equation 𝗑 𝑑𝑦 + 2𝑦 = 𝗑⁴.

A body at an unknown temperature is placed in a room which is held

at a constant temperature of 32° F. If after 10 minutes the temperature of the

body is 0° F and after 20 minutes the temperature of the body is 10° F, find the

unknown initial temperature.

 5. If the function y = y(x) is such that x dy dx + 2y = x cos x, use the integrating-factor method to show that y = sin x + 2 cos x /x − 2 sin x/x^2 + c/x^2 , where c is an arbitrary constant

 4. Find the general solution of the differential equation dy/dx + y cot x = 1, recalling that cot x = cos x / sin x 

 3. Find the particular solution of the linear equation dy/dx + 1/x y = x if y(1) = 0