Решение уравнений 1 и 2 порядка

[latex]1)\; \; y'=5x^3-6x^2+1\; ,\; \; y(-1)=1\\\\\int dy=\int (5x^3-6x^2+1)dx\\\\y=\frac{5}{4}x^4-2x^3+x+C\\\\y(-1)=\frac{5}{4}+2-1+C=\frac{9}{4}+C=2,25+C=1\\\\C=-1,25\\\\y=\frac{5}{4}x^4-2x^3+x-1,25[/latex] [latex]2)\; \; y''+4x=5\\\\y''=5-4x\\\\y'=\int (5-4x)dx=-\frac{1}{4}\cdot \frac{(5-4x)^2}{2}+C_1\\\\y=\int (-\frac{1}{8}\cdot (5-4x)^2+C_1)dx\\\\y=-\frac{1}{8}\cdot (-\frac{1}{4})\cdot \frac{(5-4x)^3}{3}+C_1x+C_2\\\\y=\frac{1}{96}\cdot (5-4x)^3+C_1x+C_2[/latex]