37.24 problem 1146

Internal problem ID [3830]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 37
Problem number: 1146.
ODE order: 1.
ODE degree: -1.

CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]

Solve \begin {gather*} \boxed {\ln \left (y^{\prime }\right )+4 y^{\prime } x -2 y=0} \end {gather*}

Solution by Maple

Time used: 0.031 (sec). Leaf size: 67

dsolve(ln(diff(y(x),x))+4*x*diff(y(x),x)-2*y(x) = 0,y(x), singsol=all)
 

\begin{align*} y \relax (x ) = \frac {\ln \left (\frac {-1+\sqrt {16 c_{1} x +1}}{4 x}\right )}{2}-\frac {1}{2}+\frac {\sqrt {16 c_{1} x +1}}{2} \\ y \relax (x ) = \frac {\ln \left (-\frac {1+\sqrt {16 c_{1} x +1}}{4 x}\right )}{2}-\frac {1}{2}-\frac {\sqrt {16 c_{1} x +1}}{2} \\ \end{align*}

Solution by Mathematica

Time used: 0.116 (sec). Leaf size: 36

DSolve[Log[y'[x]]+4 x y'[x]-2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\text {ProductLog}\left (4 x e^{2 y(x)}\right )-\log \left (\text {ProductLog}\left (4 x e^{2 y(x)}\right )+2\right )-2 y(x)=c_1,y(x)\right ] \]