29.30.27 problem 887

Internal problem ID [5467]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 887
Date solved : Monday, January 27, 2025 at 11:24:52 AM
CAS classification : [[_homogeneous, `class G`], _rational, _dAlembert]

\begin{align*} 4 x {y^{\prime }}^{2}+4 y^{\prime } y&=1 \end{align*}

✓ Solution by Maple

Time used: 0.054 (sec). Leaf size: 149

dsolve(4*x*diff(y(x),x)^2+4*y(x)*diff(y(x),x) = 1,y(x), singsol=all)
 

\begin{align*} \frac {2 x \left (\frac {3 c_{1} \left (y \left (x \right )-\sqrt {y \left (x \right )^{2}+x}\right ) \sqrt {\frac {-y \left (x \right )+\sqrt {y \left (x \right )^{2}+x}}{x}}}{2}+3 y \left (x \right )^{2}-3 y \left (x \right ) \sqrt {y \left (x \right )^{2}+x}+x \right )}{3 \left (y \left (x \right )-\sqrt {y \left (x \right )^{2}+x}\right )^{2}} &= 0 \\ \frac {2 x \left (-3 c_{1} \left (y \left (x \right )+\sqrt {y \left (x \right )^{2}+x}\right ) \sqrt {\frac {-2 y \left (x \right )-2 \sqrt {y \left (x \right )^{2}+x}}{x}}+3 y \left (x \right )^{2}+3 y \left (x \right ) \sqrt {y \left (x \right )^{2}+x}+x \right )}{3 \left (y \left (x \right )+\sqrt {y \left (x \right )^{2}+x}\right )^{2}} &= 0 \\ \end{align*}

✓ Solution by Mathematica

Time used: 60.236 (sec). Leaf size: 4057

DSolve[4 x (D[y[x],x])^2+4 y[x] D[y[x],x]==1,y[x],x,IncludeSingularSolutions -> True]
 

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