Practice Introduction to Differential Equations in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
An equation that contains an unknown function and one or more of its derivatives. Solving a DE means finding the function(s) that satisfy the equation.
An algebraic equation like x^2 = 4 asks 'what number satisfies this?' A differential equation like \frac{dy}{dx} = 2x asks 'what function has this derivative?' The answer isn't a number but a family of functions: y = x^2 + C.
Example 1
easyVerify y = 3e^{2x} solves y' = 2y, and find the particular solution with y(0) = 5.
Example 2
mediumFind the general and particular (y(0)=4) solution to y' = 3x^2+1.
Example 3
easyVerify that y = \sin x + 2\cos x satisfies y'' + y = 0.
Example 4
mediumFind the particular solution to y' = -2y with y(0)=3.