Solve the differential equation subject to the initial condition using Integra dr Axy - e-2x^2 = 0; y(0) = 5 dx Oy = xe^-2x^2 + 5 Oy = (x + 5)e^(-2x) y = xe^(2x+5) y = (x + 5)e^(-2x)
Added by April B.
Close
Step 1
To solve it, we need to find an integrating factor. The integrating factor is given by: IF = e^{\int A dx} = e^{\int x dx} = e^{x^2/2} Now, multiply the entire differential equation by the integrating factor: (e^{x^2/2}y)' = e^{x^2/2}e^{-2x^2} Integrate both Show more…
Show all steps
Your feedback will help us improve your experience
Erika Bustos and 64 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Solve the given differential equation by undetermined coefficients. $y^{\prime \prime}+2 y^{\prime}=2 x+5-e^{-2 x}$
Higher-Order Differential Equations
Undetermined Coefficients
Solve the differential equation. $$\frac{d y}{d x}=\left(e^{x}+5\right)^{2}$$
Integration Techniques, L’Hopital’s Rule, and Improper Integrals
Basic Integration Rules
Solve the given differential equation by undetermined coefficients. $$y^{\prime \prime}-y=x^{2} e^{x}+5$$
Undetermined Coeficients—Annihilator Approach
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD