4.18.4 \(x y'(x)^2+4 y'(x)-2 y(x)=0\)

ODE
\[ x y'(x)^2+4 y'(x)-2 y(x)=0 \] ODE Classification

[_rational, _dAlembert]

Book solution method
No Missing Variables ODE, Solve for \(x\)

Mathematica ✓
cpu = 30.997 (sec), leaf count = 40

\[\text {Solve}\left [\left \{\text {K$\$$1655} x+4=\frac {2 y(\text {K$\$$1655})}{\text {K$\$$1655}},y(x)=\frac {\text {K$\$$1655} \left (c_1 \text {K$\$$1655}+4 \text {K$\$$1655} \log (\text {K$\$$1655})+8\right )}{(\text {K$\$$1655}-2)^2}\right \},\{y(x),\text {K$\$$1655}\}\right ]\]

Maple ✓
cpu = 0.019 (sec), leaf count = 43

\[ \left \{ [x \left ( {\it \_T} \right ) ={\frac {-4\,{\it \_T}+8\,\ln \left ( {\it \_T} \right ) +{\it \_C1}}{ \left ( -2+{\it \_T} \right ) ^{2}}},y \left ( {\it \_T} \right ) ={\frac {{\it \_T}\, \left ( 8\,{\it \_T}\,\ln \left ( {\it \_T} \right ) +16+ \left ( {\it \_C1}-16 \right ) {\it \_T} \right ) }{2\, \left ( -2+{\it \_T} \right ) ^{2}}}] \right \} \] Mathematica raw input

DSolve[-2*y[x] + 4*y'[x] + x*y'[x]^2 == 0,y[x],x]

Mathematica raw output

Solve[{4 + K$1655*x == (2*y[K$1655])/K$1655, y[x] == (K$1655*(8 + K$1655*C[1] + 
4*K$1655*Log[K$1655]))/(-2 + K$1655)^2}, {y[x], K$1655}]

Maple raw input

dsolve(x*diff(y(x),x)^2+4*diff(y(x),x)-2*y(x) = 0, y(x),'implicit')

Maple raw output

[x(_T) = 1/(-2+_T)^2*(-4*_T+8*ln(_T)+_C1), y(_T) = 1/2*_T*(8*_T*ln(_T)+16+(_C1-1
6)*_T)/(-2+_T)^2]