how to solve ode y”=3y’-10y y(0)=1 y'(0)=-1

Question : solve ode y”=3y’-10y y(0)=1 y'(0)=-1Solution :Given homogeneous linear differential equation \[y”=3y’-10y\] \[ y(0)=1,\ y'(0)=-1\] \[y”-3y’+10y=0 \] (1) So it’s auxiliary equation is \[\lambda^2-3\lambda+10=0\] \[\lambda^2-5\lambda+2\lambda+10=0\] \[\lambda\left(\lambda-5\right)+2\left(\lambda-5\right)=0\] \[\left(\lambda+2\right)\left(\lambda-5\right)=0\] It’s roots are \[\lambda_1=-2 , \lambda_2=5\] Hence the general solution of the…

This Question has been answered. 

Please Subscribe to See Answer or To Get Homework Help