71.17.4 problem 5

Internal problem ID [14560]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 7. Systems of First-Order Differential Equations. Exercises page 329
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 08:25:30 PM
CAS classification : system_of_ODEs

\begin{align*} y_{1}^{\prime }\left (x \right )&=\frac {2 y_{1} \left (x \right )}{x}-\frac {y_{2} \left (x \right )}{x^{2}}-3+\frac {1}{x}-\frac {1}{x^{2}}\\ y_{2}^{\prime }\left (x \right )&=2 y_{1} \left (x \right )+1-6 x \end{align*}

With initial conditions

\begin{align*} y_{1} \left (1\right ) = -2\\ y_{2} \left (1\right ) = -5 \end{align*}

✓ Solution by Maple

Time used: 1.222 (sec). Leaf size: 19

dsolve([diff(y__1(x),x) = 2*y__1(x)/x-y__2(x)/x^2-3+1/x-1/x^2, diff(y__2(x),x) = 2*y__1(x)+1-6*x, y__1(1) = -2, y__2(1) = -5], singsol=all)
 

\begin{align*} y_{1} \left (x \right ) &= -2 x \\ y_{2} \left (x \right ) &= -1+x \left (-5 x +1\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 19

DSolve[{D[ y1[x],x]==2*y1[x]/x-y2[x]/x^2-3+1/x-1/x^2,D[ y2[x],x]==2*y1[x]+1-6*x},{y1[1]==-2,y2[1]==-5},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
 

\begin{align*} \text {y1}(x)\to -2 x \\ \text {y2}(x)\to -5 x^2+x-1 \\ \end{align*}