10.2.35 problem 36

Internal problem ID [1163]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 36
Date solved : Monday, January 27, 2025 at 04:37:37 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} x^{2}+3 y x +y^{2}-x^{2} y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

dsolve((x^2+3*x*y(x)+y(x)^2)-x^2* diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\frac {x \left (\ln \left (x \right )+c_1 +1\right )}{\ln \left (x \right )+c_1} \]

✓ Solution by Mathematica

Time used: 0.154 (sec). Leaf size: 28

DSolve[(x^2+3*x*y[x]+y[x]^2)-x^2* D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {x (\log (x)+1+c_1)}{\log (x)+c_1} \\ y(x)\to -x \\ \end{align*}