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Question Number 214813 by ajfour last updated on 20/Dec/24

Help me solve this (dy/dx)+(a/y)+b(√x)=0

$${Help}\:{me}\:{solve}\:{this} \\ $$$$\frac{{dy}}{{dx}}+\frac{{a}}{{y}}+{b}\sqrt{{x}}=\mathrm{0} \\ $$

Commented by ajfour last updated on 20/Dec/24

https://youtu.be/H53vv0XMRs4?si=eeFguqQqwBJDXTTU

Answered by issac last updated on 20/Dec/24

(dy/dx)+(a/y)+b(√(x ))=(y/x)+(a/y)+b(√x)=0 xy((y/x)+(a/y)+b(√x))=0 y^2 +ax+bxy(√x)=0 y=((−bx(√x)±(√(b^2 x^3 −4ax)))/2)

$$\frac{\cancel{\mathrm{d}}{y}}{\cancel{\mathrm{d}}{x}}+\frac{{a}}{{y}}+{b}\sqrt{{x}\:}=\frac{{y}}{{x}}+\frac{{a}}{{y}}+{b}\sqrt{{x}}=\mathrm{0} \\ $$$${xy}\left(\frac{{y}}{{x}}+\frac{{a}}{{y}}+{b}\sqrt{{x}}\right)=\mathrm{0} \\ $$$${y}^{\mathrm{2}} +{ax}+{bxy}\sqrt{{x}}=\mathrm{0} \\ $$$${y}=\frac{−{bx}\sqrt{{x}}\pm\sqrt{{b}^{\mathrm{2}} {x}^{\mathrm{3}} −\mathrm{4}{ax}}}{\mathrm{2}} \\ $$

Commented by ajfour last updated on 20/Dec/24