= x2/3 y² +1 Ôx Ôy (c) Find the general solution of PDE:

Q: 2xy"+ oy' ty :0

A: Given:- 2xy"+6y'+y=0   2xy"+6y'+y=0...(1) y"+62xy'+12xy=0 y"+3xy'+12xy=0...(2) Comparing equation(2)…

Q: Given y'+y = 0, y(3) = 2. Solve this initial value problem for x = 3(0.5)5 using Euler's %3D !!…

A:

Q: Find the solution to the initial-value problem. dy = y³xe*, y(0) = 1 dx II

A:

Q: (b) Obtain the general solution of y^ prime prime +2y^ prime +y=e^ -x ln x on (0, ∞)

A: To find- Obtain the general solution of y'' + 2y' + y = e-xlnx on 0, ∞.

Q: dy xe*- dx -In y Solve the initial value problem , y(0)=1. 6.2

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Q: Find an explicit solution of the given initial-value problem. V1- y? dx V1-х2 dy %3D0, у(0): у%3D х…

A:

Q: Find the particular solution of the initial value problem: dy 3x2(y? + 1), dx y(0) = 1 %3D

A: We can find the answer as below.

Q: If = you want to solve y' Ay, y(0) = 1 (A 2?

A: As per the question we are given a linear differential equation as : y' = λy  ;  y(0) = 1 Now if we…

Q: Given the initial value problem y' = x² + xy with y(0) = 1.5. %3D i. Use the RK-4 to estimate the…

A:

Q: Find the general solution of the DE y’’ = xsin(x)

A: Topic = Differential equation

Q: Find te goneral solution: (x e - ) dy

A: We have to find the general solution of the differential equation ey-yexdx+xey-exdy=0 .

Q: Solve the initial value problem.

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Q: 1. Find the general solution of dy dx + y = x

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Q: Solve the initial value problem dy + X, x > 0; y(2) = 0 x3 dx

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Q: xy²dx + e*dy = 0

A: Given differential equation is xy2dx+exdy=0

Q: y(x + y+ 1)dæ = –(x+ 2y)dy,

A: To solve the below initial value problem. yx+y+1dx=−x+2ydy,   y0=1

Q: Find the general solution of dy xy = 1+ y?

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Q: (2y +4x)dx- xydy=0 y(1)= -2

A:

Q: Solve the initial value problem using the method of indefinite coefficients. d'y d²y -5+4y 16x+ 20e"…

A: Given that the differential equation is d2ydx2-5dydx+4y=16x+20ex with y(0)=0, y'(0)=1. The axillary…

Q: 4. Solve the 2nd-order Homogeneous D.E. y" – 36y = 0

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Q: 1. Find the general solution of dy dx +y=x

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Q: Find the particular solution determined by the initial condition. ds 16t2 + 5t – 5; s(0) = 100 dt

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Q: For the initial value problem  y'=x+1 y(-1) = 1 use the Cauchy-Euler Method to approximate y(1)…

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: Find an explicit solution of the given initial-value problem. V1- dx - V1 - x² dy = 0, y(0) V1- V3x…

A: Given: The given equation is 1-y2dx-1-x2dy=0,y(0)=22

Q: Solve for general solution using Bernoulli method x?y dx + (1+ x³)dy = 0

A: x2ydx+(1+x3)dy=0dydx+(x21+x3)y=0.which is in the form of burnouli's equationdydx+Py=Qynhere P=x21+x3…

Q: Solve the initial-value problem using the undetermined coefficients at the condition, y(0) = 2,…

A:

Q: a. Solve the initial value problem dx with y(0) = 4. Use t as the variable of integration in the…

A: I have solved using separation of vsriable method

Q: 4. Find the solution of (x²+6y²)dx – 4xydy=0 when x=1, y=1. Use Substitution Method.

A:

Q: Give the general solution of y = 5ex-y. a) Oy = ex + C b) Oe-y = 5e* + C c) Oy = In(e* + C) d) O e =…

A: We will find out the required general solution.

Q: dy-5+4y =16x+20e" dx ; y(0) = 0, y'(0) =1 dx

A: Given differential equation d2ydx2-5dydx+4y=16x+20ex. The Auxiliary equation is…

Q: Solve the initial value problem dy/dx= 1+x+x^2/2, with y=1 when x=0.

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Q: 2(y- 4X²)dx + x dy =o SOLVE THE PROBLEM USING INTEGRATION FUNCTION

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Q: Find the solution of the initial value problem in explicit form: dy 7+ 12x x > 0, y(1) = 4 dx xy?

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Q: 2. Find the particular solution of (xy + x)dx = (x?y² + x² + y² + 1)dy satisfying the initial…

A: Using Variable Separable Method

Q: In finding y(1.2) for the initial value problem(VP) = x° +y, y(1) = 1 by the R-K method of order 4,…

A:

Q: Solve the homogenous diff equation of; xdx . (y+1) dy y³ e-x = 0

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Q: e general solution to the DE  is(6x+y2)dx+y(2x-3y)dy

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Q: Solve the given initial-value problem. dx y = 5y², x(9) = 1 dy

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Q: Consider the DE y' = (6x + y + 8)², y(0) = 1 Solve it numerically using Euler's method (n=4) to…

A:

Q: 2. Find the particular solution of Vx2 + y2 )dx – x dy = 0 ; y = 1 when x V3. -

A: Given differential equations homogeneous differential equation of first order we will do the…

Q: Solve the given initial value problem using the method of exactness. xy dy+(2x2+3y2-20) dy=0, y(0)=1

A: The equation is in the form Mdx+Ndy =0, with M = xy and N = 2x2+3y2-20.Check the exactness of the…

Q: 4. Find the general solution of this DE using INSPECTION. dadx + aydy +(X² + y?)dx = 0

A:

Q: Find the solution to the initial-value problem, 0.015ydx + dy = 0; y(0) = 10. Find an interval of…

A: It is a basic linear equation of first order  the standard equation is in the form of  dydx+Py=Q…

Q: (2xy +y) dx + (x²- x ) dy = 0

A: Given: (2xy+y)dx+(x2-x)dy=0, y(0)=e

Q: Solve the initial value problem. dy + 5xy = 8x, y(0) = - 6 dx y =

A: topic - differential equations

Q: Use the Adams-Bashforth-Moulton method to approximate y(0.4), where y(x) is the solution of the…

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Q: Xy"+y=0. solve by forbenius method.

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Q: Solve the initial-value problem. dy dx3 . for x20 with y(0) =3 The solution to the initial-value…

A: To find: The solution of initial value problem. Given: The differential equation is dydx=x33 for x≥0…

Q: y-2y=xy, y(0)=22

A: Using bernoulli 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.