28.1.127 problem 150

Internal problem ID [4433]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 150
Date solved : Monday, January 27, 2025 at 09:17:14 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Chini]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 98

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

\[ \frac {\left (-x^{2}+4 y \left (x \right )\right ) \ln \left (\frac {x^{2}-4 y \left (x \right )}{x^{2}}\right )+2 i \left (x^{2}-4 y \left (x \right )\right ) \arctan \left (2 \sqrt {-\frac {y \left (x \right )}{x^{2}}}\right )-4 i \sqrt {-\frac {y \left (x \right )}{x^{2}}}\, x^{2}+4 \left (-c_{1} +2 \ln \left (x \right )\right ) y \left (x \right )+x^{2} \left (c_{1} -2 \ln \left (x \right )-2\right )}{x^{2}-4 y \left (x \right )} = 0 \]

✓ Solution by Mathematica

Time used: 0.108 (sec). Leaf size: 49

DSolve[2*D[y[x],x]+x==4*Sqrt[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [4 \left (\frac {4}{4 \sqrt {\frac {y(x)}{x^2}}+2}+2 \log \left (4 \sqrt {\frac {y(x)}{x^2}}+2\right )\right )=-8 \log (x)+c_1,y(x)\right ] \]