Question and Answers Forum

All Questions      Topic List

Differential Equation Questions

Previous in All Question      Next in All Question      

Previous in Differential Equation      Next in Differential Equation      

Question Number 82883 by jagoll last updated on 26/Feb/20

[(e^(−2(√x)) /(√x))−(y/(√x)) ] .(dx/dy) = 1 , x ≠ 0

$$\left[\frac{\mathrm{e}^{−\mathrm{2}\sqrt{\mathrm{x}}} }{\sqrt{\mathrm{x}}}−\frac{\mathrm{y}}{\sqrt{\mathrm{x}}}\:\right]\:.\frac{\mathrm{dx}}{\mathrm{dy}}\:=\:\mathrm{1}\:,\:\mathrm{x}\:\neq\:\mathrm{0} \\ $$

Answered by john santu last updated on 26/Feb/20

⇒(dy/dx) = (e^(−2(√x)) /(√x)) − (y/(√x))  (dy/dx) + ((1/(√x))) y = (e^(−2(√x)) /(√x))  IF = e^(∫ (1/(√x)) dx)  = e^(2(√x))    ⇒ y.e^(2(√x))   = ∫  (e^(−2(√x)) /(√x)) × e^(2(√x))  dx  ⇒y.e^(2(√x))  = ∫ (1/(√x)) dx  ⇒ y.e^(2(√x))  = 2(√x) + C

$$\Rightarrow\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{e}^{−\mathrm{2}\sqrt{\mathrm{x}}} }{\sqrt{\mathrm{x}}}\:−\:\frac{\mathrm{y}}{\sqrt{\mathrm{x}}} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}\:+\:\left(\frac{\mathrm{1}}{\sqrt{\mathrm{x}}}\right)\:\mathrm{y}\:=\:\frac{\mathrm{e}^{−\mathrm{2}\sqrt{\mathrm{x}}} }{\sqrt{\mathrm{x}}} \\ $$$$\mathrm{IF}\:=\:\mathrm{e}\:^{\int\:\frac{\mathrm{1}}{\sqrt{\mathrm{x}}}\:\mathrm{dx}} \:=\:\mathrm{e}^{\mathrm{2}\sqrt{\mathrm{x}}} \: \\ $$$$\Rightarrow\:\mathrm{y}.\mathrm{e}^{\mathrm{2}\sqrt{\mathrm{x}}} \:\:=\:\int\:\:\frac{\mathrm{e}^{−\mathrm{2}\sqrt{\mathrm{x}}} }{\sqrt{\mathrm{x}}}\:×\:\mathrm{e}^{\mathrm{2}\sqrt{\mathrm{x}}} \:\mathrm{dx} \\ $$$$\Rightarrow\mathrm{y}.\mathrm{e}^{\mathrm{2}\sqrt{\mathrm{x}}} \:=\:\int\:\frac{\mathrm{1}}{\sqrt{\mathrm{x}}}\:\mathrm{dx} \\ $$$$\Rightarrow\:\mathrm{y}.\mathrm{e}^{\mathrm{2}\sqrt{\mathrm{x}}} \:=\:\mathrm{2}\sqrt{\mathrm{x}}\:+\:\mathrm{C} \\ $$$$ \\ $$

Commented by john santu last updated on 26/Feb/20

haha...i will check sir

$$\mathrm{haha}...\mathrm{i}\:\mathrm{will}\:\mathrm{check}\:\mathrm{sir} \\ $$

Commented by jagoll last updated on 26/Feb/20

soory sir. i wrote the problem . sir  john is right. thank you sir w and  john

$$\mathrm{soory}\:\mathrm{sir}.\:\mathrm{i}\:\mathrm{wrote}\:\mathrm{the}\:\mathrm{problem}\:.\:\mathrm{sir} \\ $$$$\mathrm{john}\:\mathrm{is}\:\mathrm{right}.\:\mathrm{thank}\:\mathrm{you}\:\mathrm{sir}\:\mathrm{w}\:\mathrm{and} \\ $$$$\mathrm{john} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com