Solve the given initial-value problem.\ y" + x(y')² = 0, y(1) = 4, y'(1) = 2\ y =
Added by Ricky B.
Close
Step 1
We can do this by using the chain rule: y'' = (dy'/dx)' = (dy'/dt)/(dx/dt) = (dy'/dt)/(y') Substituting this into the original equation, we get: y t (dy'/dt)^2/(y')^2 = 0 Multiplying both sides by (y')^2 and simplifying, we get: y t (dy'/dt)^2 = 0 This Show more…
Show all steps
Your feedback will help us improve your experience
Mukesh Devi and 89 other Calculus 1 / AB 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 initial value problem for y(t): 4y" + 12y' = -9y, y(0) = -1, y'(0) = 1/2
Gopesh V.
Solve the given initial-value problem. $$y^{\prime}+2 y=2 u_{1}(t), \quad y(0)=1$$.
The Laplace Transform and Some Elementary Applications
The Second Shifting Theorem
Solve the initial-value problem. $$ \frac{d y}{d t}+y=2, \quad y(0)=1 $$
MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS
First-Order Differential Equations and Applications
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Watch the video solution with this free unlock.
EMAIL
PASSWORD