4.18.30 \((x+1) y'(x)^2=y(x)\)

ODE
\[ (x+1) y'(x)^2=y(x) \] ODE Classification

[[_homogeneous, `class C`], _rational, _dAlembert]

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

Mathematica
cpu = 0.0186776 (sec), leaf count = 52

\[\left \{\left \{y(x)\to -c_1 \sqrt {x+1}+\frac {c_1^2}{4}+x+1\right \},\left \{y(x)\to c_1 \sqrt {x+1}+\frac {c_1^2}{4}+x+1\right \}\right \}\]

Maple
cpu = 0.02 (sec), leaf count = 40

\[ \left \{ y \relax (x ) =0,[x \left ({\it \_T} \right ) ={\frac {-{{\it \_T}}^{2}+{\it \_C1}+2\,{\it \_T}}{ \left ({\it \_T}-1 \right ) ^{2}}},y \left ({\it \_T} \right ) ={\frac {{{\it \_T}}^{2} \left ({\it \_C1}+1 \right ) }{ \left ({\it \_T}-1 \right ) ^{2}}}] \right \} \] Mathematica raw input

DSolve[(1 + x)*y'[x]^2 == y[x],y[x],x]

Mathematica raw output

{{y[x] -> 1 + x - Sqrt[1 + x]*C[1] + C[1]^2/4}, {y[x] -> 1 + x + Sqrt[1 + x]*C[1
] + C[1]^2/4}}

Maple raw input

dsolve((1+x)*diff(y(x),x)^2 = y(x), y(x),'implicit')

Maple raw output

y(x) = 0, [x(_T) = 1/(_T-1)^2*(-_T^2+_C1+2*_T), y(_T) = _T^2*(_C1+1)/(_T-1)^2]