Solve the given differential equation.

${y}^{\prime}=\frac{5{x}^{2}-1}{5+8y}$

${y}^{\prime}=\frac{5{x}^{2}-1}{5+8y}$

Luciano Webster
2022-07-26
Answered

Solve the given differential equation.

${y}^{\prime}=\frac{5{x}^{2}-1}{5+8y}$

${y}^{\prime}=\frac{5{x}^{2}-1}{5+8y}$

You can still ask an expert for help

Makenna Lin

Answered 2022-07-27
Author has **16** answers

Given:

$\frac{dy}{dx}=\frac{5{x}^{2}-1}{5+9y}$

variable septerution

$\int (5+8y)dy=\int (5{x}^{2}-1)dx\phantom{\rule{0ex}{0ex}}5y+\frac{8{y}^{2}}{2}=\frac{5{x}^{3}}{3}-x+C\phantom{\rule{0ex}{0ex}}5y+4{y}^{2}=\frac{5}{3}{x}^{3}-x+C\phantom{\rule{0ex}{0ex}}15y+12{y}^{2}=5{x}^{3}-4x+3C$

where c= constant

$\frac{dy}{dx}=\frac{5{x}^{2}-1}{5+9y}$

variable septerution

$\int (5+8y)dy=\int (5{x}^{2}-1)dx\phantom{\rule{0ex}{0ex}}5y+\frac{8{y}^{2}}{2}=\frac{5{x}^{3}}{3}-x+C\phantom{\rule{0ex}{0ex}}5y+4{y}^{2}=\frac{5}{3}{x}^{3}-x+C\phantom{\rule{0ex}{0ex}}15y+12{y}^{2}=5{x}^{3}-4x+3C$

where c= constant

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