IB Mathematics Applications & Interpretation Question Type 1: Finding the General Solution to Linear Coupled Differential Equations with Real and Distinct Eigenvalues Exercises

Find the particular solution to the system of differential equations $$\frac{dx}{dt}=4x+y,\frac{dy}{dt}=2x+3y$$ given that $x(0)=0$ and $y(0)=3$.

Find the general solution to the system $$\frac{dx}{dt}=7x+3y,\frac{dy}{dt}=4x+2y$$

Find the general solution to the system $$\frac{dx}{dt}=6x+2y,\frac{dy}{dt}=3x+5y$$

Find the general solution to the system of differential equations: $$\frac{\text{d}x}{\text{d}t}=4x+y$$ $$\frac{\text{d}y}{\text{d}t}=2x+3y$$

Find the particular solution to the system $$\{\begin{array}{l}\frac{dx}{dt}=2x+y\\ \frac{dy}{dt}=3y\end{array}$$ given $x(0)=4$ and $y(0)=2$.

Find the general solution to the system of differential equations: $$\frac{dx}{dt}=2x+y,\frac{dy}{dt}=3y$$

Find the particular solution to the system $$\frac{dx}{dt}=x+2y,\frac{dy}{dt}=4y$$ given $x(0)=3$ and $y(0)=1$.

Find the particular solution to the system $$\frac{dx}{dt}=6x+2y,\frac{dy}{dt}=3x+5y$$ given $x(0)=-1$ and $y(0)=2$.

Find the particular solution to the system of differential equations $$\begin{array}{rl}\frac{dx}{dt}& =5x+2y\\ \frac{dy}{dt}& =2x+2y\end{array}$$ given that $x(0)=1$ and $y(0)=0$.

Find the general solution to the system $$\{\begin{array}{l}\frac{dx}{dt}=5x+2y\\ \frac{dy}{dt}=2x+2y\end{array}$$

Find the particular solution to the system $$\frac{dx}{dt}=2x+3y,\frac{dy}{dt}=-y$$ given $x(0)=2$ and $y(0)=1$.

Find the general solution to the system of differential equations $$\{\begin{array}{l}\frac{dx}{dt}=x+2y\\ \frac{dy}{dt}=4y\end{array}$$