Internal problem ID [39]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.4. Separable equations. Page 43
Problem number: 14.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {1+\sqrt {x}}{1+\sqrt {y}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x) = (1+x^(1/2))/(1+y(x)^(1/2)),y(x), singsol=all)
\[ x +\frac {2 x^{\frac {3}{2}}}{3}-y \relax (x )-\frac {2 y \relax (x )^{\frac {3}{2}}}{3}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 4.468 (sec). Leaf size: 789
DSolve[y'[x]== (1+x^(1/2))/(1+y[x]^(1/2)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (4 \left (2 \sqrt {x}+3\right ) x \left (4 x^{3/2}+6 x-9\right )+8 \sqrt {\left (2 x^{3/2}+3 x-1+3 c_1\right ) \left (2 x^{3/2}+3 x+3 c_1\right ){}^3}+48 c_1 \left (2 \sqrt {x}+3\right ) x+27+72 c_1{}^2-108 c_1\right ){}^{2/3}+3 \sqrt [3]{4 \left (2 \sqrt {x}+3\right ) x \left (4 x^{3/2}+6 x-9\right )+8 \sqrt {\left (2 x^{3/2}+3 x-1+3 c_1\right ) \left (2 x^{3/2}+3 x+3 c_1\right ){}^3}+48 c_1 \left (2 \sqrt {x}+3\right ) x+27+72 c_1{}^2-108 c_1}-8 \left (2 \sqrt {x}+3\right ) x+9-24 c_1}{4 \sqrt [3]{4 \left (2 \sqrt {x}+3\right ) x \left (4 x^{3/2}+6 x-9\right )+8 \sqrt {\left (2 x^{3/2}+3 x-1+3 c_1\right ) \left (2 x^{3/2}+3 x+3 c_1\right ){}^3}+48 c_1 \left (2 \sqrt {x}+3\right ) x+27+72 c_1{}^2-108 c_1}} \\ y(x)\to \frac {1}{16} \left (\frac {\left (2+2 i \sqrt {3}\right ) \left (16 x^{3/2}+24 x-9+24 c_1\right )}{\sqrt [3]{4 \left (2 \sqrt {x}+3\right ) x \left (4 x^{3/2}+6 x-9\right )+8 \sqrt {\left (2 x^{3/2}+3 x-1+3 c_1\right ) \left (2 x^{3/2}+3 x+3 c_1\right ){}^3}+48 c_1 \left (2 \sqrt {x}+3\right ) x+27+72 c_1{}^2-108 c_1}}+2 i \left (\sqrt {3}+i\right ) \sqrt [3]{4 \left (2 \sqrt {x}+3\right ) x \left (4 x^{3/2}+6 x-9\right )+8 \sqrt {\left (2 x^{3/2}+3 x-1+3 c_1\right ) \left (2 x^{3/2}+3 x+3 c_1\right ){}^3}+48 c_1 \left (2 \sqrt {x}+3\right ) x+27+72 c_1{}^2-108 c_1}+12\right ) \\ y(x)\to \frac {1}{16} \left (\frac {\left (2-2 i \sqrt {3}\right ) \left (16 x^{3/2}+24 x-9+24 c_1\right )}{\sqrt [3]{4 \left (2 \sqrt {x}+3\right ) x \left (4 x^{3/2}+6 x-9\right )+8 \sqrt {\left (2 x^{3/2}+3 x-1+3 c_1\right ) \left (2 x^{3/2}+3 x+3 c_1\right ){}^3}+48 c_1 \left (2 \sqrt {x}+3\right ) x+27+72 c_1{}^2-108 c_1}}-2 \left (1+i \sqrt {3}\right ) \sqrt [3]{4 \left (2 \sqrt {x}+3\right ) x \left (4 x^{3/2}+6 x-9\right )+8 \sqrt {\left (2 x^{3/2}+3 x-1+3 c_1\right ) \left (2 x^{3/2}+3 x+3 c_1\right ){}^3}+48 c_1 \left (2 \sqrt {x}+3\right ) x+27+72 c_1{}^2-108 c_1}+12\right ) \\ \end{align*}