9.24 problem 1879

Internal problem ID [9458]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1879.
ODE order: 1.
ODE degree: 1.

Solve \begin {align*} x^{\prime }\relax (t )&=\frac {-2 x \relax (t )+2 y \relax (t )+t}{t}\\ y^{\prime }\relax (t )&=-\frac {-t^{2}+x \relax (t )+5 y \relax (t )}{t} \end {align*}

Solution by Maple

Time used: 0.079 (sec). Leaf size: 54

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

\[ x \relax (t ) = \frac {2 t^{6}+9 t^{5}+30 c_{1} t +30 c_{2}}{30 t^{4}} \] \[ y \relax (t ) = -\frac {-8 t^{6}+3 t^{5}+30 c_{1} t +60 c_{2}}{60 t^{4}} \]

Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 58

DSolve[{t*x'[t]+2*(x[t]-y[t])==t,t*y'[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*}