First-Order Linear Differential Equations; Solutions Suggested by the Equation dydx=(x+y+1)2
First-Order Linear Differential Equations; Solutions Suggested by the Equation
Answer & Explanation
We have given the differential equation as . To solve this differential equation, we have to use substitution to convert the equation into the separable differential equation because separable equations are easy to solve.
So substitute . First, differentiate with respect to x to find the expression for .
Now, do substitution and simplify the differential equation.
Now, integrate both sides of and evaluate the integral. Use the formula .
[Substitute back ]
Hence, the solution of the given differential equation is , where C is an integral constant.
from eqn(1) and (2)
The given differential equation is
Integrating, we get
Which is the required solution.