Question

Solve Differential Equation
y' = 4 x + 7 y

Answer 1

`y'=4x+7y`

`y'-7y=4x`

`e^(-7x)y'-7e^(-7x)y=4xe^(-7x)`

`(\mathrm d)/(\mathrm dx)\left[e^(-7x)y\right]=4xe^(-7x)`

`e^(-7x)y=\displaystyle\int4xe^(-7x)\,\mathrm dx`

`e^(-7x)y=-\frac47xe^(-7x)-\frac4{49}e^(-7x)+C`

`y=-\frac47x-\frac4{49}+Ce^(7x)`