60.9.20 problem 1875

Internal problem ID [11874]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 8, system of first order odes
Problem number : 1875
Date solved : Tuesday, January 28, 2025 at 06:23:55 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )+\left (a x \left (t \right )+b y \left (t \right )\right ) f \left (t \right )&=g \left (t \right )\\ \frac {d}{d t}y \left (t \right )+\left (c x \left (t \right )+d y \left (t \right )\right ) f \left (t \right )&=h \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 3.227 (sec). Leaf size: 3921

dsolve([diff(x(t),t)+(a*x(t)+b*y(t))*f(t)=g(t),diff(y(t),t)+(c*x(t)+d*y(t))*f(t)=h(t)],singsol=all)
 

\begin{align*} \text {Expression too large to display} \\ \text {Expression too large to display} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.737 (sec). Leaf size: 3095

DSolve[{D[x[t],t]+(a*x[t]+b*y[t])*f[t]==g[t],D[y[t],t]+(c*x[t]+d*y[t])*f[t]==h[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

Too large to display