71.7.13 problem 17

Internal problem ID [14434]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.3, page 71
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 06:30:59 AM
CAS classification : [_separable]

\begin{align*} y \left (2 x -1\right )+x \left (1+x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 12

dsolve(y(x)*(2*x-1)+x*(x+1)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{1} x}{\left (x +1\right )^{3}} \]

✓ Solution by Mathematica

Time used: 0.074 (sec). Leaf size: 38

DSolve[y[x]*(2*x-1)+x*(x+1)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \exp \left (\int _1^x\frac {1-2 K[1]}{K[1]^2+K[1]}dK[1]\right ) \\ y(x)\to 0 \\ \end{align*}