60.9.24 problem 1879

Internal problem ID [11878]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 8, system of first order odes
Problem number : 1879
Date solved : Tuesday, January 28, 2025 at 06:23:57 PM
CAS classification : system_of_ODEs

\begin{align*} t \left (\frac {d}{d t}x \left (t \right )\right )+2 x \left (t \right )-2 y \left (t \right )&=t\\ t \left (\frac {d}{d t}y \left (t \right )\right )+x \left (t \right )+5 y \left (t \right )&=t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.079 (sec). Leaf size: 53

dsolve([t*diff(x(t),t)+2*(x(t)-y(t))=t,t*diff(y(t),t)+x(t)+5*y(t)=t^2],singsol=all)
 

\begin{align*} x \left (t \right ) &= \frac {2 t^{6}+9 t^{5}+30 c_{2} t +30 c_{1}}{30 t^{4}} \\ y \left (t \right ) &= -\frac {-8 t^{6}+3 t^{5}+30 c_{2} t +60 c_{1}}{60 t^{4}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 58

DSolve[{t*D[x[t],t]+2*(x[t]-y[t])==t,t*D[y[t],t]+x[t]+5*y[t]==t^2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \frac {c_1}{t^4}+\frac {c_2}{t^3}+\frac {1}{30} t (2 t+9) \\ y(t)\to -\frac {-8 t^6+3 t^5+30 c_2 t+60 c_1}{60 t^4} \\ \end{align*}