Final answer:
To solve the given differential equation, we can use the method of integrating factor. The solution is y = (3³/9 + )^(-7).
Step-by-step explanation:
To solve the differential equation x dy/dx + 7y = 3x², we can use the method of integrating factor. The integrating factor for this equation is ^( ) which is equal to ^(∫7 ) = ^(7). Multiplying both sides of the differential equation by ^(7), we get: ^(7) / + 7^(7) = 3²^(7). This can be rewritten as /(^(7)) = 3²^(7). Integrating both sides gives us the solution = (3³/9 + )^(-7).