Internal problem ID [6025]
Book: Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam
Publishing Co. NY. 6th edition. 1981.
Section: CHAPTER 16. Nonlinear equations. Section 94. Factoring the left member. EXERCISES
Page 309
Problem number: 12.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (-y+4 x \right ) \left (y^{\prime }\right )^{2}+6 \left (x -y\right ) y^{\prime }+2 x -5 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.029 (sec). Leaf size: 55
dsolve((4*x-y(x))*diff(y(x),x)^2+6*(x-y(x))*diff(y(x),x)+2*x-5*y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = c_{1}-x \\ y \relax (x ) = -\frac {4 c_{1} x -\sqrt {-12 c_{1} x +1}-1}{2 c_{1}} \\ y \relax (x ) = -\frac {4 c_{1} x +\sqrt {-12 c_{1} x +1}-1}{2 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.373 (sec). Leaf size: 79
DSolve[(4*x-y[x])*(y'[x])^2+6*(x-y[x])*y'[x]+2*x-5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\frac {1}{2} \text {RootSum}\left [\sqrt {7} \text {$\#$1}^4+22 \text {$\#$1}^4-32 \sqrt {7} \text {$\#$1}^3-464 \text {$\#$1}^2+256 \sqrt {7} \text {$\#$1}-64 \sqrt {7}+1408\&,\frac {\sqrt {7} \text {$\#$1}^3 \log \left (-\frac {4 \text {$\#$1} y(x)}{x}-\sqrt {7} \text {$\#$1}+3 \text {$\#$1}+4 \sqrt {\frac {8 y(x)^2}{x^2}-\frac {12 y(x)}{x}+1}\right )+22 \text {$\#$1}^3 \log \left (-\frac {4 \text {$\#$1} y(x)}{x}-\sqrt {7} \text {$\#$1}+3 \text {$\#$1}+4 \sqrt {\frac {8 y(x)^2}{x^2}-\frac {12 y(x)}{x}+1}\right )-\sqrt {7} \text {$\#$1}^3 \log \left (\frac {4 y(x)}{x}+\sqrt {7}-3\right )-22 \text {$\#$1}^3 \log \left (\frac {4 y(x)}{x}+\sqrt {7}-3\right )-32 \sqrt {7} \text {$\#$1}^2 \log \left (-\frac {4 \text {$\#$1} y(x)}{x}-\sqrt {7} \text {$\#$1}+3 \text {$\#$1}+4 \sqrt {\frac {8 y(x)^2}{x^2}-\frac {12 y(x)}{x}+1}\right )+32 \sqrt {7} \text {$\#$1}^2 \log \left (\frac {4 y(x)}{x}+\sqrt {7}-3\right )+112 \sqrt {7} \text {$\#$1} \log \left (-\frac {4 \text {$\#$1} y(x)}{x}-\sqrt {7} \text {$\#$1}+3 \text {$\#$1}+4 \sqrt {\frac {8 y(x)^2}{x^2}-\frac {12 y(x)}{x}+1}\right )-232 \text {$\#$1} \log \left (-\frac {4 \text {$\#$1} y(x)}{x}-\sqrt {7} \text {$\#$1}+3 \text {$\#$1}+4 \sqrt {\frac {8 y(x)^2}{x^2}-\frac {12 y(x)}{x}+1}\right )-112 \sqrt {7} \text {$\#$1} \log \left (\frac {4 y(x)}{x}+\sqrt {7}-3\right )+232 \text {$\#$1} \log \left (\frac {4 y(x)}{x}+\sqrt {7}-3\right )}{\sqrt {7} \text {$\#$1}^3+22 \text {$\#$1}^3-24 \sqrt {7} \text {$\#$1}^2-232 \text {$\#$1}+64 \sqrt {7}}\&\right ]+2 \log \left (\frac {4 y(x)}{x}+\sqrt {7}-3\right )-\log \left (\frac {4 \sqrt {7} y(x)}{x}-3 \sqrt {7}+7\right )=-\log (x)+c_1,y(x)\right ] \\ \text {Solve}\left [\frac {1}{2} \text {RootSum}\left [\sqrt {7} \text {$\#$1}^4+22 \text {$\#$1}^4+32 \sqrt {7} \text {$\#$1}^3-464 \text {$\#$1}^2-256 \sqrt {7} \text {$\#$1}-64 \sqrt {7}+1408\&,\frac {\sqrt {7} \text {$\#$1}^3 \log \left (-\frac {4 \text {$\#$1} y(x)}{x}-\sqrt {7} \text {$\#$1}+3 \text {$\#$1}+4 \sqrt {\frac {8 y(x)^2}{x^2}-\frac {12 y(x)}{x}+1}\right )+22 \text {$\#$1}^3 \log \left (-\frac {4 \text {$\#$1} y(x)}{x}-\sqrt {7} \text {$\#$1}+3 \text {$\#$1}+4 \sqrt {\frac {8 y(x)^2}{x^2}-\frac {12 y(x)}{x}+1}\right )-\sqrt {7} \text {$\#$1}^3 \log \left (\frac {4 y(x)}{x}+\sqrt {7}-3\right )-22 \text {$\#$1}^3 \log \left (\frac {4 y(x)}{x}+\sqrt {7}-3\right )+32 \sqrt {7} \text {$\#$1}^2 \log \left (-\frac {4 \text {$\#$1} y(x)}{x}-\sqrt {7} \text {$\#$1}+3 \text {$\#$1}+4 \sqrt {\frac {8 y(x)^2}{x^2}-\frac {12 y(x)}{x}+1}\right )-32 \sqrt {7} \text {$\#$1}^2 \log \left (\frac {4 y(x)}{x}+\sqrt {7}-3\right )+112 \sqrt {7} \text {$\#$1} \log \left (-\frac {4 \text {$\#$1} y(x)}{x}-\sqrt {7} \text {$\#$1}+3 \text {$\#$1}+4 \sqrt {\frac {8 y(x)^2}{x^2}-\frac {12 y(x)}{x}+1}\right )-232 \text {$\#$1} \log \left (-\frac {4 \text {$\#$1} y(x)}{x}-\sqrt {7} \text {$\#$1}+3 \text {$\#$1}+4 \sqrt {\frac {8 y(x)^2}{x^2}-\frac {12 y(x)}{x}+1}\right )-112 \sqrt {7} \text {$\#$1} \log \left (\frac {4 y(x)}{x}+\sqrt {7}-3\right )+232 \text {$\#$1} \log \left (\frac {4 y(x)}{x}+\sqrt {7}-3\right )}{\sqrt {7} \text {$\#$1}^3+22 \text {$\#$1}^3+24 \sqrt {7} \text {$\#$1}^2-232 \text {$\#$1}-64 \sqrt {7}}\&\right ]+2 \log \left (\frac {4 y(x)}{x}+\sqrt {7}-3\right )-\log \left (\frac {4 \sqrt {7} y(x)}{x}-3 \sqrt {7}+7\right )=-\log (x)+c_1,y(x)\right ] \\ \end{align*}