Use Euler’s method to find 4 approximate values of the solution to the given initial value problem. Use h = 0.2 dy/dx=x2+y2   y(2)=5

Q: (a)((x+1)² – y²)ª– (2(x+1)y – 10(x+1)²) = 0 dx

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Q: dy 2x + 1 y(-2) = -1. dx 2y

A: To solve the IVP: dydx=2x+12y, where y-2=-1. Solution: Separating the variables of the given…

Q: 3 de + 4 €²x³² + = ²0 dt

A: The given differential equation is ,                 dxdt+4x5t3 + xt = 0 (.)  Bernoulli equation :…

Q: Use Picard's method to solve dx - Find y3(1)? -xy, y (0) = 1

A: Solution :-

Q: 는 (1-5)~ dx =C 1+2e dy + 2 Find the gereral solution.

A: To solve the differential equation:  1+2eyxdy+2eyx1−yxdx=01+2eyxdy=−2eyx1−yxdx⇒dydx=2eyx−1+yx1+2eyx

Q: e the following nth-order equation using the variation of parameter method: y"-3y"+3y'-y=

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Q: Solve the following differential equation using the parameter variation method: x²y" – xy – y = x²

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Q: solve using non-exact (x+4y3)dy - ydx = 0

A: Solving the non exact differential equation

Q: SOLVE FOR CL is constant : A² jª (a²-2₁²x² + x²) dx = 1

A: The given integral is A2∫-aaa4-2a2x2+x4dx=1. We have to find the value of a.

Q: Solve the particular solution of (xª + y³)dx – 2x° dy= 0 when x = 2, y = 3. -

A: We can rewrite the given equation as,  (xy+y3)dx = 2x3dy xydx+y3dx = 2x3dy

Q: Solve the Bernoulli's DE: 2x3 y = y(y? + 3x2). %3D

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Q: Solve the initial value problem: + 4 y 20 dx y(0) = 2.

A: Follow the steps below to solve an initial value problem by the variable separation method. First,…

Q: dy Solve the differential equation = dx = -5x√y. √y = -5x² + Cor y = 0 √y = -5x² + Cor y = 0 2 √y =…

A: Here is the solution:

Q: - 4. 3y(x² − 1)dx + (x³ + 8y − 3x)dy = 0; when x = 0, y = 1

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Q: Verify that y = x² – 1 is a solution of (y')* + y² = -1. %3D

A: Given;            y=x2-1 is a solution of y'4+y2=-1 We compute the first derivative.…

Q: Solve dy/dx + 2y = 4, y(0) = 3 by one of the usual methods. Solve same the problem by Picard’s…

A: Integrating factor method for solving a differtial equation  Consider the differtial equation…

Q: z

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Q: Solve the D.E (X+1) =x(y'い) dメ

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Q: Given: 3. __ydy 1+ y² || dx X when y(2) = 3 Answers: 3.y = 1 10x² - 4

A: To prove that, y=1210x2-4, is a solution of the following initial value problem.y dy1+y2=dxx, when…

Q: (2xy-ey)dx + (x2-xey)dy = 0 Find the general solution of this differantial equation.

A: (2xy-ey)dx + (x2-xey)dy = 0…

Q: 2. Find the linear approximation to y = sinh (3x) at x=2. State your answer in both exact form and…

A: Find the linear approximation of f(x) at a point x=2

Q: 3x²y dx (x³ + y³)dy = 0, y(1) = y(1) = -2 -

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Q: Given dy/dx = xy + 2x, the solution to this DE is Select one: O a. O b. O C. O d. O e. y= ±x -…

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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.