15.20.7 problem 7

Internal problem ID [3315]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 38, page 173
Problem number : 7
Date solved : Monday, January 27, 2025 at 07:33:18 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.067 (sec). Leaf size: 35

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

\begin{align*} y \left (x \right ) &= \sqrt {2}\, x \\ y \left (x \right ) &= -\sqrt {2}\, x \\ y \left (x \right ) &= \frac {2 c_{1}^{2}+x^{2}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 63

DSolve[2*x+D[y[x],x]*x==2*D[y[x],x]*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{34} \left (\left (17+\sqrt {17}\right ) \log \left (\frac {4 y(x)}{x}+\sqrt {17}-1\right )-\left (\sqrt {17}-17\right ) \log \left (-\frac {4 y(x)}{x}+\sqrt {17}+1\right )\right )=-\log (x)+c_1,y(x)\right ] \]