Find the general solution of the equation: xy – y = x²e=x (x > 0)

Q: Find the solution fo (x^3-y^3)dx + xy^2

A: Here we have,  (x3-y3)dx+xy2dy=0⇒(x3-y3)dx=xy2dy⇒dydx=(x3-y3)xy2 ..............(1) Which is a…

Q: Solve the homogenous diff equation of; y' = y sec x

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Q: Find the solution. 2y" - 3y' + y = 0 (A By = c,e 1- ©y = c,e Dy =c,e

A: Find roots of  characteristic  equation  of given differential equation .If roots are real and…

Q: Find the particular solution of (y + Vx² + y²)dx – xdy; when x = v3, y = 1

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Q: Q3: Solve (x + y)dx - x dy = 0

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Q: dy - y = e2*y³ dx

A: Let's Solve,

Q: Solve for the value of C in the equation: (3xy +2y) dx + (2x<y + x) dy = 0 when y(1) = 2.

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Q: Q2: solve the equation 3 dx 2х * dy y

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Q: Solve: (4x3y−18x2−y)dx + (x4+3y2−x)dy = 0 a) Check for exactness b) If the equation is exact,…

A: Exact differential equation

Q: dx J x* – 1

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Q: dy x(x+ 1) Solve and find the particular solution when y(1) = 3 %3D dr

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Q: 4.2(х — у)dx + (3х — у — 1)dy 3 0

A: Let's find.

Q: y'e² 3-2х y' = y– xy

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Q: Solve the equation dy --y=-y*(x² +x+1); y(1)=2. dx

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Q: Using the variation of parameters, find the particular solution of (D2 +1)y = secx

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Q: Find the solution for: y' – x e = 0 using separation of variables.

A: Solution of differential equation

Q: (x + 2y – 1)dx + 3(x + 2y)dy = 0

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Q: Solve y' = x2 + y for x=1, taking h=0.2, y(0)=0. Find y(1)

A: Given differential equation                                         y'=x2+y with initial value…

Q: Solve the equation using Variation of Parameters (D² + 1) y = tan x

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Q: (b) Solve y" + e*yf + (1 + x²)y = 0, %3D x = 0, if y(0) = 1; y'(0) = 0. %3D

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Q: What is the solution for y(t)?

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Q: Solve for the value of C in the equation: dy – (y + xy³)dx = 0 when y(0) = 1

A: The given differential equation dy-y+xy5dx=0dydx=y+xy5dydx-y=xy5 It is first-order Bernoulli's…

Q: Find the General and Particular solution of = 3y ; y= 3,when x = dx

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Q: 3. (x – 4y – 9)dx + (4x + y – 2)dy = 0 -

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Q: 3 y = (x² +1) ² Find day dx ²

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Q: y varies directly as x can be modeled by the equation______ , where k is called the_______ .

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Q: Solve the diffrencial equation.  4x3 y4 - Lny+(y/x)/-4x4 y3 + (x/y)-Lnx = dy/dx

A: Mdx + Ndy =0if ∂M∂y =∂N∂xIt's exact diffrential equation and then solution :∫y constMdx + ∫(terms of…

Q: Find the solution 7. (x + 4y³)dy - ydx = 0

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Q: [1+ (x + y)²]dx + [1+ x(x + y)]dy = 0

A: Given: 1+x+y2dx+1+xx+ydy=0

Q: Solve the equation 3(y+1)dx-(x+y +3)dy =0.

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Q: Q9// find the general solution (sec³x + (cotx)y)dx + (Insinx)dy = 0

A: Answer and explanation is given below...

Q: Solve the equation 3(y+1)dx-(x+ y +3)dy =0.

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Q: Solve the equation (2y°-x°) dx t 3x*y dy =0 y + p(x) y= 9 (x) y" independent y dependent

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Q: Find the solution. ,dy --y²=2xy dx A y B y = -(- -1 D 2x x-2

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Q: Find the point of intersection and solve the equation (x − 4y − 9)dx + (4x + y − 2)dy = 0

A: The given equation is x-4y-9dx+4x+y-2dy=0. The equation of the straight line are x-4y-9=04x+y-2=0.…

Q: Find and in terms of t. dx2 x= -9 sint, y = cost dx dx2

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Q: 2. (2x + y – 4)dx + (x – 3y + 12)dy = 0 -

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Q: Find y = (2x²² -6) ⁹ dy اده

A: We can find the derivative as below.

Q: y = e² -Vx sec 6x 3

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Q: Solve the Fo (lowin) D-E e* y+2 ey =2X 2X

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Q: Solve by making the equation into an exact equation. (2 – x - y) dx + (3 +x + y) dy = 0

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Q: Q1: solve the equation (y +x )dy + (x - y )dx = 0

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Q: Solve for the General Solution. ( x csc y/x-y) dx + x dy = 0

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Q: y^2dy=x(xdy-ydx)e^x/y solve using homogeneous equations (diff eq)

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Q: Solve the IVP d'y = 4sec 2x tan 2x, y' (0) = 4, y(0) =-1 dx2

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Q: ey-x y' = 1+ e2y ,y(0) = 3 %3D (h=0.01) .What is the error in the solution?

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Q: Solve the equation 3(y+1)dx-(x+y+3)dy =0.

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Q: Solve y dx - (axdy + a²dx) = x²(y² - a²)dy

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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.