Internal problem ID [2176]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 29(b).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x +\frac {y}{2}}{\frac {x}{2}-y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.22 (sec). Leaf size: 30
dsolve([diff(y(x),x)=(x+1/2*y(x))/(1/2*x-y(x)),y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\sin \left (\RootOf \left (4 \textit {\_Z} -4 \ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )-8 \ln \relax (x )+4 \ln \relax (2)-\pi \right )\right ) x}{\cos \left (\RootOf \left (4 \textit {\_Z} -4 \ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )-8 \ln \relax (x )+4 \ln \relax (2)-\pi \right )\right )} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 42
DSolve[{y'[x]==(x+1/2*y[x])/(1/2*x-y[x]),{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\log \left (\frac {y(x)^2}{x^2}+1\right )-\text {ArcTan}\left (\frac {y(x)}{x}\right )=\frac {1}{4} (4 \log (2)-\pi )-2 \log (x),y(x)\right ] \]