The indicated function y1(x) is a solution of the given differential equation. Use reduction of order or formula e-SP(x) dx dx Y2 = Y1(x) / y? (x) (5) as instructed, to find a second solution y2(x). (1 – 2x – x2)y" + 2(1 + x)y' – 2y = 0; Y1 = x + 1 Y2 =

Q: Solve by applying "Differential Equation using Substitution Suggested by the Equation"…

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Q: Use an appropriate substitution (4-5 a cos² to solve the differential equation (-) ) ª dx - x dy =…

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Q: (a) 2xy? + x²y' = y², y(1) = = -1 (а) Зу(2? — 1) + (»3 + 8y — За) dy (b) 4x?3 dy гу* + 2 dæ (e) xy'…

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Q: Solve the exact differential equation: (2x+1+2xy) dx + (x2 +  4y3) dy = 0

A: (2x+1+2xy ) dx + (x2 + 4y3) dy = 0  on comparing with   Mdx + Ndy  , we get ,       M =…

Q: 2x dy 2х. -y = x² - x; y(4) =2 dx

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Q: Solve the Exact differential equation ydx-xdy + 3x³y²e¹¹dx=0

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Q: The differential equation 3x?yy' – 3x5 = y?can be changed to linear by the substitution (a) v = y?…

A: Put y=vx So, none of these is correct option.

Q: Solve using the non-exact linear differential equation  [ytan(x)(cos(2x))-1]dx+csc(2x)dy=0 when…

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Q: Q2. Factor out the differential equation and find the general solution.…

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Q: f(x) = 2x + 1; ¹/f = x² d.x

A: Solution: Given, f(x) = 2x + 1;  dfdx=x2 We have to check whether f(x) = 2x+1 is the solution to the…

Q: Find the differential equation of the following function (x + y – 1)dx + (2x + 2y + 1)dy = 0 a. x +…

A: Given differential equation is  (x+y-1)dx+(2x+2y+1)dy=0

Q: y' + (2 tan x)y = cos³ x = COS" X

A: The correct answer is option (I) , i.e.  y = (cos²x)(c+sinx) The detailed solution is as follows…

Q: Solve the initial value problem below using the method of Laplace transforms. - 4t y" - 16y = 16t –…

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Q: Q12// Solve the differential equation (x² – 3y²)dx – 2x²dy = 0

A: We have to find General solution of given differential equation using substitution Method.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.