What is the solution for y^{''}+y=x^2+1,y(0)=3,y(1)=0 ?

The solution for y^{''}+y=x^2+1,y(0)=3,y(1)=0 is y=4cos(x)-(4cos(1)sin(x))/(sin(1))+x^2-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}+y=x^2+1,y(0)=3,y(1)=0

y^{^{''}} + y = x^{2} + 1, y (0) = 3, y (1) = 0

y = 4 cos (x) - \frac{4 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

Solution steps

y^{''} (x) + y = x^{2} + 1

Solve linear ODE:

y = 4 cos (x) - \frac{4 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

y = 4 cos (x) - \frac{4 cos ( 1 ) sin ( x )}{sin ( 1 )} + x^{2} - 1

What is the solution for y^{''}+y=x^2+1,y(0)=3,y(1)=0 ?
The solution for y^{''}+y=x^2+1,y(0)=3,y(1)=0 is y=4cos(x)-(4cos(1)sin(x))/(sin(1))+x^2-1