First-Order Linear Differential Equations; Solutions Suggested by the Equation dydx=(x+y+1)2
Daniell Phillips
Answered
2021-12-26
First-Order Linear Differential Equations; Solutions Suggested by the Equation
Answer & Explanation
Hector Roberts
Expert
2021-12-27Added 31 answers
Step 1
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.
Step 2
So substitute . First, differentiate with respect to x to find the expression for .
Now, do substitution and simplify the differential equation.
Step 3
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.
sirpsta3u
Expert
2021-12-28Added 42 answers
(1)
Let. (2)
from eqn(1) and (2)
. Answer.
Vasquez
Expert
2022-01-09Added 457 answers
The given differential equation is ...(i)
Let
Integrating, we get
Which is the required solution.