Question
Show that the solution of the initial value problem$$y^{\prime}=x+y, \quad y\left(x_{0}\right)=y_{0}$$is$$y=-1-x+\left(1+x_{0}+y_{0}\right) e^{x-x_{0}}.$$
Step 1
$$ Show more…
Show all steps
Your feedback will help us improve your experience
Clarissa Noh and 94 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Solve the given initial-value problem. $$\left(x+y e^{y / x}\right) d x-x e^{y / x} d y=0, \quad y(1)=0$$
First-Order Differential Equations
Solutions by Substitutions
Find the solution of the given initial value problem. $$ y^{\prime}(x)=x / y(x) \quad y(0)=1 $$
Applications of the Integral
First Order Differential Equations—Separable Equations
Solve the given initial-value problem. $$y^{\prime \prime}+y^{\prime}=x, \quad y(0)=1, y^{\prime}(0)=0$$
Higher-Order Differential Equations
Undetermined Coeficients—Annihilator Approach
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD