Internal problem ID [6312]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Chini]
Solve \begin {gather*} \boxed {y^{\prime }-\sqrt {y}-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 65
dsolve(diff(y(x),x)=sqrt(y(x))+x,y(x), singsol=all)
\[ \frac {4 \arctanh \left (\sqrt {\frac {y \relax (x )}{x^{2}}}\right )}{3}-\frac {2 \arctanh \left (2 \sqrt {\frac {y \relax (x )}{x^{2}}}\right )}{3}-\frac {\ln \left (-\frac {x^{2}-4 y \relax (x )}{x^{2}}\right )}{3}-\frac {2 \ln \left (-\frac {2 \left (x^{2}-y \relax (x )\right )}{x^{2}}\right )}{3}-2 \ln \relax (x )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 60.15 (sec). Leaf size: 555
DSolve[y'[x]==Sqrt[y[x]]+x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (3 x^2+\frac {e^{3 c_1} x \left (8+e^{3 c_1} x^3\right )}{\sqrt [3]{8 \sqrt {-e^{24 c_1} \left (-1+e^{3 c_1} x^3\right ){}^3}+e^{12 c_1} \left (-e^{6 c_1} x^6+20 e^{3 c_1} x^3+8\right )}}+e^{-6 c_1} \sqrt [3]{8 \sqrt {-e^{24 c_1} \left (-1+e^{3 c_1} x^3\right ){}^3}+e^{12 c_1} \left (-e^{6 c_1} x^6+20 e^{3 c_1} x^3+8\right )}\right ) \\ y(x)\to \frac {1}{72} \left (54 x^2+\frac {\left (-9-9 i \sqrt {3}\right ) e^{3 c_1} x \left (8+e^{3 c_1} x^3\right )}{\sqrt [3]{8 \sqrt {-e^{24 c_1} \left (-1+e^{3 c_1} x^3\right ){}^3}+e^{12 c_1} \left (-e^{6 c_1} x^6+20 e^{3 c_1} x^3+8\right )}}+9 i \left (\sqrt {3}+i\right ) e^{-6 c_1} \sqrt [3]{8 \sqrt {-e^{24 c_1} \left (-1+e^{3 c_1} x^3\right ){}^3}+e^{12 c_1} \left (-e^{6 c_1} x^6+20 e^{3 c_1} x^3+8\right )}\right ) \\ y(x)\to \frac {1}{72} \left (54 x^2+\frac {9 i \left (\sqrt {3}+i\right ) e^{3 c_1} x \left (8+e^{3 c_1} x^3\right )}{\sqrt [3]{8 \sqrt {-e^{24 c_1} \left (-1+e^{3 c_1} x^3\right ){}^3}+e^{12 c_1} \left (-e^{6 c_1} x^6+20 e^{3 c_1} x^3+8\right )}}-9 \left (1+i \sqrt {3}\right ) e^{-6 c_1} \sqrt [3]{8 \sqrt {-e^{24 c_1} \left (-1+e^{3 c_1} x^3\right ){}^3}+e^{12 c_1} \left (-e^{6 c_1} x^6+20 e^{3 c_1} x^3+8\right )}\right ) \\ \end{align*}