If the equation consists of ordinary derivatives only with respect to a single variable, which is...
Fundamentals of Differential EquationsAdd \sin \left( x+y \right) to both sides of the given equation. \frac{dy}{dx}=\sin \left( x+y...
Fundamentals of Differential EquationsFind the rate at which Substance S enters into the container. \left( 8\ \text{L/min} \right)\left(...
Fundamentals of Differential EquationsSubstitute 0 for b and 0 for {{F}_{\text{ext}}}\left( t \right) into the equation...
Fundamentals of Differential EquationsSubstitute D-1 for A and {{t}^{3}}-8 for y into the given expression, and then use the distributive...
Fundamentals of Differential EquationsDivide both sides of the given differential equation by x .
Fundamentals of Differential EquationsLet f\left( t \right)=t . Apply the Laplace transform F\left( s \right)=\int_{0}^{\infty...
Fundamentals of Differential EquationsSubstitute 0 for x and 1 for y into the given equation, and solve. \begin{aligned} {y}'\left(...
Fundamentals of Differential EquationsRewrite the right side of each equation as the dot product of the coefficient matrix and the...
Fundamentals of Differential Equations