60.1.471 problem 474

Internal problem ID [10485]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 474
Date solved : Monday, January 27, 2025 at 07:55:12 PM
CAS classification : [[_homogeneous, `class C`], _rational, _dAlembert]

\begin{align*} 2 y {y^{\prime }}^{2}-\left (4 x -5\right ) y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.190 (sec). Leaf size: 119

dsolve(2*y(x)*diff(y(x),x)^2-(4*x-5)*diff(y(x),x)+2*y(x) = 0,y(x), singsol=all)
 

\begin{align*} y &= x -\frac {5}{4} \\ y &= -x +\frac {5}{4} \\ y &= 0 \\ y &= \frac {\sqrt {4 c_{1} +2 \sqrt {-c_{1} \left (4 x -5\right )^{2}}}}{2} \\ y &= -\frac {\sqrt {4 c_{1} +2 \sqrt {-c_{1} \left (4 x -5\right )^{2}}}}{2} \\ y &= \frac {\sqrt {4 c_{1} -2 \sqrt {-c_{1} \left (4 x -5\right )^{2}}}}{2} \\ y &= -\frac {\sqrt {4 c_{1} -2 \sqrt {-c_{1} \left (4 x -5\right )^{2}}}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.616 (sec). Leaf size: 160

DSolve[2*y[x] - (-5 + 4*x)*D[y[x],x] + 2*y[x]*D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -i \sqrt {2} e^{\frac {c_1}{2}} \sqrt {4 x-5+8 e^{c_1}} \\ y(x)\to i \sqrt {2} e^{\frac {c_1}{2}} \sqrt {4 x-5+8 e^{c_1}} \\ y(x)\to -\frac {1}{4} i e^{\frac {c_1}{2}} \sqrt {8 x-10+e^{c_1}} \\ y(x)\to \frac {1}{4} i e^{\frac {c_1}{2}} \sqrt {8 x-10+e^{c_1}} \\ y(x)\to 0 \\ y(x)\to \frac {5}{4}-x \\ y(x)\to x-\frac {5}{4} \\ \end{align*}