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Solve the differential equation: (tan^-1y - x)dy = (1 + y^2)dx?

Solve the differential equation: (tan^-1y - x)dy = (1 + y^2)dx?

WebNov 17, 2024 · Solve the differential equation (tan^-1 x - y)dx = (1 + x^2)dy. ← Prev Question Next Question →. 0 votes. 92.1k views. asked Nov 17, 2024 in Mathematics by Samantha (39.3k points) Solve the differential … WebMar 16, 2024 · So we use the integrating factor method 𝑑𝑦/𝑑𝑥 = ( (1 + 𝑦^2))/ (tan^ (−1) y − x) This is not of the form 𝑑𝑦/𝑑𝑥+𝑃𝑦=𝑄 ∴ We need to find 𝑑𝑥/𝑑𝑦 𝑑𝑥/𝑑𝑦 = (tan^ (−1)𝑦 − 𝑥)/ (1 + 𝑦^2 ) 𝑑𝑥/𝑑𝑦 = tan^ (−1)𝑦/ (1 + 𝑦^2 ) − 𝑥/ (1 + 𝑦^2 ) 𝑑𝑥/𝑑𝑦 + 𝑥/ (1 + 𝑦^2 ) − (tan^ (−1)𝑦 )/ (1 … construction cleanup services in phoenix az WebSolve: y - xdy/dx = a (y^2+dy/dx) Class 12 >> Maths >> Differential Equations >> Solving Differential Equations - Variable Separable Method >> Solve: y - xdy/dx = a (y^2+dy/dx) Question Solve: y−x dxdy=a(y 2+ dxdy) Medium Solution Verified by Toppr or, ln∣y∣−ln∣1−ay∣=ln∣(a+x)∣+lnc [ Where c is integrating constant] or, 1−ayy =c(a+x). WebLearn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=y(1+y). Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Integrate both sides of the differential equation, the left side with respect to y, … doge click bot telegram termux WebGiven that(1+y2)dx=(tan−1y−x)dy ⇒dxdy=tan−1y1+y2−x1+y2 ⇒dxdy+x1+y2=tan−1y1+y2The differential equation is in the form dxdy+P (y)x=Q(y) where P (y)=11+y2 and Q(y)=tan−1y1+y2So, Integration factor, (I.F.)=e∫11+y2dy=etan−1y∴solution is given as : x×etan−1y=∫etan−1y×tan−1y1+y2dy+CPut tan−1y=t⇒11+y2dy=dt. ∴xetan ... WebLearn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=1+y^2. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Integrate both sides of the differential equation, the left side with respect to y, … construction clean up services richmond WebAug 1, 2016 · 1 2y −1 ⋅ dy dx = 1. integrating. ∫ 1 2y −1 dy dx dx = ∫ dx. ∫ 1 2y −1 dy = ∫ dx. 1 2 ln(2y − 1) = x +C. ln(2y −1) = 2x + C. 2y −1 = e2x+C = Ce2x.

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