Question

Please Solve the following differential equation y'−2⋅y=−9+(−10)⋅x Given: y(0) = 13

Answer 1

y'=4

Answer 2

y=9+10x+y',
13=9+10(0)+y'
y'=13-9
y'=4

Answer 3

\[y'-2y=-9-10x.\ |y(0)=13.=>\] \[\int\limits y '-2y=\int\limits -9-10x=>\]
\[y-y^2+K_1=-9x-5x^2+K_2=>\] \[y(1-y)=-9x-5x^2+K_1+K_2=>\]\[If \ y(0)=13,\ => y(1-y)=13.(1-13)=-9.0-5.0^2+K=>\]\[ ∴K=-156\]\[y(1-y)=-9x-5x^2-156\]