71.18.4 problem 4

Internal problem ID [14578]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 8. Linear Systems of First-Order Differential Equations. Exercises 8.3 page 379
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 06:43:46 AM
CAS classification : system_of_ODEs

\begin{align*} y_{1}^{\prime }\left (x \right )&=2 x y_{1} \left (x \right )-x^{2} y_{2} \left (x \right )+4 x\\ y_{2}^{\prime }\left (x \right )&={\mathrm e}^{x} y_{1} \left (x \right )+3 \,{\mathrm e}^{-x} y_{2} \left (x \right )-\cos \left (3 x \right ) \end{align*}

✗ Solution by Maple

dsolve([diff(y__1(x),x)=2*x*y__1(x)-x^2*y__2(x)+4*x,diff(y__2(x),x)=exp(x)*y__1(x)+3*exp(-x)*y__2(x)-cos(3*x)],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[ y1[x],x]==2*x*y1[x]-x^2*y2[x]+4*x,D[ y2[x],x]==Exp[x]*y1[x]+3*Exp[-x]*y2[x]-Cos[3*x]},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
 

Not solved