Internal problem ID [7062]
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]
\[ \boxed {y^{\prime }-\sqrt {\frac {y+1}{y^{2}}}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.329 (sec). Leaf size: 148
dsolve([diff(y(x),x)=sqrt( (1+y(x))/y(x)^2),y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (1+i \sqrt {3}\right ) \left (-12 \sqrt {2}\, x +9 x^{2}+\sqrt {\left (-12 \sqrt {2}\, x +9 x^{2}-8\right ) \left (3 x -2 \sqrt {2}\right )^{2}}\right )^{\frac {2}{3}}-4 i \sqrt {3}-4 \left (-12 \sqrt {2}\, x +9 x^{2}+\sqrt {\left (-12 \sqrt {2}\, x +9 x^{2}-8\right ) \left (3 x -2 \sqrt {2}\right )^{2}}\right )^{\frac {1}{3}}+4}{4 \left (-12 \sqrt {2}\, x +9 x^{2}+\sqrt {\left (-12 \sqrt {2}\, x +9 x^{2}-8\right ) \left (3 x -2 \sqrt {2}\right )^{2}}\right )^{\frac {1}{3}}} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 123
DSolve[{y'[x]==Sqrt[ (1+y[x])/y[x]^2],y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{4} \left (1+i \sqrt {3}\right ) \sqrt [3]{9 x^2+\sqrt {81 x^4-216 \sqrt {2} x^3+288 x^2-64}-12 \sqrt {2} x}+\frac {i \left (\sqrt {3}+i\right )}{\sqrt [3]{9 x^2+\sqrt {81 x^4-216 \sqrt {2} x^3+288 x^2-64}-12 \sqrt {2} x}}+1 \]