Internal problem ID [6309]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{\prime }-\sqrt {\frac {y+1}{y^{2}}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.656 (sec). Leaf size: 148
dsolve([diff(y(x),x)=sqrt( (1+y(x))/y(x)^2),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {\left (1+i \sqrt {3}\right ) \left (-12 x \sqrt {2}+9 x^{2}+\sqrt {\left (-12 x \sqrt {2}+9 x^{2}-8\right ) \left (3 x -2 \sqrt {2}\right )^{2}}\right )^{\frac {2}{3}}-4 i \sqrt {3}-4 \left (-12 x \sqrt {2}+9 x^{2}+\sqrt {\left (-12 x \sqrt {2}+9 x^{2}-8\right ) \left (3 x -2 \sqrt {2}\right )^{2}}\right )^{\frac {1}{3}}+4}{4 \left (-12 x \sqrt {2}+9 x^{2}+\sqrt {\left (-12 x \sqrt {2}+9 x^{2}-8\right ) \left (3 x -2 \sqrt {2}\right )^{2}}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.175 (sec). Leaf size: 122
DSolve[{y'[x]==Sqrt[ (1+y[x])/y[x]^2],y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (-1-i \sqrt {3}\right ) \sqrt [3]{9 x^2+\sqrt {9 x^2 \left (9 x^2-24 \sqrt {2} x+32\right )-64}-12 \sqrt {2} x}+\frac {-1+i \sqrt {3}}{\sqrt [3]{9 x^2+\sqrt {9 x^2 \left (9 x^2-24 \sqrt {2} x+32\right )-64}-12 \sqrt {2} x}}+1 \\ \end{align*}