Practice Problems: Laplace Translations, Part 2

Separable differential equations are arguably the easiest types of differential equations to solve. These types of DEs can be expressed as the product of two functions by separating the variables (hence the name separable differential equations). A first-order differential equation is said to be a separable differential equation if it can be expressed as follows.

\(\displaystyle\frac{dy}{dx}=f(x)g(y)\)

Notice that the function \(f(x)\) contains only the \(x\) terms, whereas \(g(y)\) is comprised of only the \(y\) terms.

Practice Problems

Determine the solution to the given separable differential equation.

\(\displaystyle \frac{dy}{dx}=e^{2x+3y}\)
\(\displaystyle \frac{dy}{dx}=(x+1)^2\)

\(\displaystyle \frac{dy}{dx}=y^2+1\)
\(\displaystyle \frac{dy}{dx}=y-y^2\)

\(\displaystyle x\frac{dy}{dx}=2y\)
\(\displaystyle \frac{dy}{dx}=\texttt{sin}(5x)\)

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Practice Problems: Laplace Translations, Part 2