−3y=2x ∴P=−3 and Q=2x IF=e∫Pdx=e∫−3dx=e−3x General solution is, y(IF)=∫Q(IF)dx+c y(e−3x)=∫2x⋅e−3xdx+c y(e−3x)=2x‌∫e−3xdx−∫(‌
d
dx
(2x)‌∫e−3xdx)dx+c =2x⋅‌
e−3x
−3
−∫2⋅‌
e−3x
−3
dx+c =‌
−2
3
xe−3x+‌
2
3
‌∫e−3xdx+6 ye−3x=‌
−2
3
e−3x(x+‌
1
3
)+c Multiply by e3x on both sides y=−‌
2
3
(x+‌
1
3
)+c⋅e3x...(i) Since, it is given that Eq. (i) passing through (1,2) 2=‌