1+1=? 95 points + brainliest!
2 answers:
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Both equations are linear, so I'll use the integrating factor method.
The first ODE
has integrating factor
In the original equation, multiply both sides by eˣ :
Observe that
d/dx [xeˣ] = eˣ + xeˣ = (x + 1) eˣ
so that the left side is the derivative of a product, namely
Integrate both sides with respect to x :
Solve for y :
Use the given initial condition to solve for C. When x = 1, y = 2, so
Then the particular solution is
The second ODE
has integrating factor
Multiply both sides of the equation by 1/(1 + x²) :
and observe that
d/dx[1/(1 + x²)] = -2x/(1 + x²)²
Then
When x = 0, y = 3, so
