29.18.7 problem 483

Internal problem ID [5081]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 18
Problem number : 483
Date solved : Monday, January 27, 2025 at 10:08:24 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 24

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

\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (2 \ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+\textit {\_Z} +4 \ln \left (x \right )+4 c_{1} \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 32

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

\[ \text {Solve}\left [\arctan \left (\frac {y(x)}{x}\right )+2 \log \left (\frac {y(x)^2}{x^2}+1\right )=-4 \log (x)+c_1,y(x)\right ] \]