### 4 Listing of problems and solutions obtained by Mathematica and Maple

4.107   $$y'(x)=\sqrt{X Y}$$

4.132   $$y'(x)=e^{y(x)}+x$$
4.133   $$y'(x)=e^{y(x)+x}$$

4.137   $$y'(x)=a f(y(x))$$

4.146   $$x y'(x)+y(x)+x=0$$

4.148   $$x y'(x)=x^3-y(x)$$

4.150   $$x y'(x)=x^m+y(x)$$

4.155   $$x y'(x)=a y(x)$$

4.231   $$(a+x) y'(x)=b x$$

4.252   $$x^2 y'(x)=a-y(x)$$

4.330   $$2 x^2 y'(x)=y(x)$$

4.407   $$\sqrt{X} y'(x)=0$$

4.420   $$y(x) y'(x)+x=0$$

4.441   $$1-y'(x)=y(x)+x$$

4.752   $$y'(x)^2=a x^n$$
4.753   $$y'(x)^2=y(x)$$
4.754   $$y'(x)^2=x-y(x)$$
4.755   $$y'(x)^2=x^2+y(x)$$

4.759   $$y'(x)^2=y(x)^2+1$$
4.760   $$y'(x)^2=1-y(x)^2$$

4.841   $$4 y'(x)^2=9 x$$

4.847   $$x y'(x)^2=a$$
4.848   $$x y'(x)^2=a-x^2$$
4.849   $$x y'(x)^2=y(x)$$

4.895   $$x^2 y'(x)^2=a^2$$

4.931   $$x^3 y'(x)^2=a$$

4.945   $$y(x) y'(x)^2=a$$

4.1021   $$y'(x)^3=a+b x$$
4.1022   $$y'(x)^3=a x^n$$
4.1023   $$y'(x)^3-y(x)+x=0$$

4.1029   $$y'(x)^3+y'(x)-y(x)=0$$

4.1031   $$y'(x)^3-7 y'(x)+6=0$$

4.1062   $$4 y'(x)^3+4 y'(x)=x$$

4.1115   $$f(x) g(x)+y'(x)^n=0$$
4.1116   $$f(x,y(x))+y'(x)^n=0$$

4.1175   $$y''(x)=0$$
4.1176   $$y''(x)=x+\sin (x)$$

4.1178   $$y''(x)=e^x x$$

4.1180   $$y''(x)+y(x)=0$$
4.1181   $$y''(x)-y(x)=0$$
4.1182   $$y''(x)+y(x)=a x$$

4.1185   $$y''(x)+y(x)=\sec (x)$$

4.1191   $$y''(x)+y(x)=e^{-x}$$

4.1195   $$y''(x)-2 y(x)=0$$

4.1197   $$y''(x)+4 y(x)=0$$

4.1201   $$y''(x)-a^2 y(x)=x+1$$
4.1202   $$y''(x)=a x+b y(x)$$

4.1207   $$y''(x)+x y(x)=0$$

4.1215   $$a x^k y(x)+y''(x)=0$$

4.1347   $$f(x) y'(x)+y''(x)=0$$

4.1353   $$x y''(x)+y(x)=0$$

4.1355   $$x y''(x)+y'(x)=0$$
4.1356   $$x y''(x)+y'(x)=x^n$$

4.1362   $$x y''(x)+2 y'(x)=0$$
4.1363   $$x y''(x)+2 y'(x)=0$$

4.1367   $$a y'(x)+x y''(x)=0$$

4.1406   $$2 x y''(x)+y'(x)=0$$

4.1420   $$x^2 y''(x)=a+b x$$
4.1421   $$x^2 y''(x)=2 y(x)$$
4.1422   $$x^2 y''(x)=6 y(x)$$
4.1423   $$x^2 y''(x)=12 y(x)$$
4.1424   $$a y(x)+x^2 y''(x)=0$$

4.1622   $$4 x^2 y''(x)+y(x)=0$$

4.1658   $$x^3 y''(x)=a+b x$$

4.1771   $$y''(x)=0$$
4.1772   $$y''(x)=a y(x)$$
4.1773   $$y''(x)=6 y(x)^2$$
4.1774   $$y''(x)=6 y(x)^2+x$$

4.1776   $$y''(x)=2 y(x)^3$$

4.1785   $$a e^{y(x)}+y''(x)=0$$
4.1786   $$y''(x)=f(y(x))$$

4.1788   $$y''(x)+y(x) y'(x)=0$$

4.1808   $$y''(x)=a y'(x)^2$$

4.1813   $$y''(x)=e^x y'(x)^2$$

4.1821   $$y''(x)=(a-x) y'(x)^3$$

4.1824   $$a y'(x)^3+y''(x)=0$$
4.1825   $$y''(x)=x y'(x)^3$$

4.1843   $$2 y''(x)=12 y(x)^2+1$$

4.1845   $$8 y''(x)+9 y'(x)^4=0$$

4.1866   $$x^2 y''(x)+y'(x)^2=0$$

4.1884   $$x^a y''(x)+y(x)^b=0$$

4.1894   $$y(x) y''(x)=a$$
4.1895   $$y(x) y''(x)=y'(x)^2$$

4.2006   $$y(x)^2 y''(x)=a$$

4.2024   $$x y(x)^2 y''(x)=a$$

4.2030   $$y(x)^3 y''(x)=a^2$$

4.2042   $$\sqrt{y(x)} y''(x)=a$$

4.2044   $$y''(x) X(x,y(x))^3=1$$

4.2050   $$y'(x) y''(x)=a^2 x$$

4.2062   $$y''(x)^2=a+b y(x)$$
4.2063   $$y''(x)^2=a+b y'(x)^2$$

4.2086   $$y'''(x)=0$$
4.2087   $$y'''(x)=\cos (x)+1$$
4.2088   $$y'''(x)+\sin (x)=0$$
4.2089   $$y'''(x)=\sin ^3(x)$$
4.2090   $$y'''(x)=y(x)$$
4.2091   $$y'''(x)=x^2+y(x)$$

4.2093   $$y'''(x)+a y(x)=0$$
4.2094   $$y'''(x)=x y(x)$$
4.2095   $$y'''(x)+y'(x)=0$$
4.2096   $$y'''(x)=y'(x)$$

4.2105   $$y'''(x)=a^2 y(x)$$

4.2144   $$y'''(x)=a y''(x)$$

4.2156   $$x y'''(x)=2$$

4.2178   $$x^3 y'''(x)=a$$

4.2211   $$y''''(x)=0$$
4.2212   $$y''''(x)=x \cos (x)$$

4.2216   $$y''''(x)+a y(x)=0$$

4.2256   $$(a+x)^2 y''''(x)=1$$

4.2271   $$y''''''(x)=0$$
4.2272   $$y''''''(x)+a y(x)=0$$

4.2274   $$y''''''''(x)=y(x)$$

4.2279   $$y^{(n)}(x)=e^x x$$

4.2298   $$y'(x)^3 y'''(x)=1$$
4.2299   $$y''(x) y'''(x)=2$$

4.2307   $$y^{(n)}(x)=f(x)$$