Find the solution of x²y" + xy-4y=0 where y(1) 0 and y (1) 4

Q: The solution of the 2" order IVP y" - y = 0, y(0) = 0 and y' (0) = 1 is

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Q: Obtain the general solution valid near the origin: х(х-2)y1+2(х-1)у - 2у %3D0

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Q: 8x²y" + 10xy' – (1+ x)y = 0

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Q: Find the general solution of the DE: y"+y' + 2y = 0

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Q: 4. xydx + (y √ x² + y²-x²) dy=0

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Q: Show that y = ex + 3xex  is a solution of y"-2y'+y=0

A: The given differential equation is,

Q: 3. Is y(x) = Cisin2x + C2cos2x, where Ci and C2 are arbitrary constants, a solution of y" + 4y = 0?…

A: Given, y''+4y=0 a second order differential equation. To show that y(x) = C1 sin 2x + C2 cos 2x is a…

Q: Obtain the general solution. xy3dx+ex^2dy=0

A: The given differential equation is xy3dx+ex2dy=0. We have to obtain a general solution.

Q: Solve the second-order equation y" + 2y' – 3y = 9x with initial condition y(0) = 0, y' (0) = 0.

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Q: ) Obtain the general solution of y" + 2y + y = e² In r

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: find general solution. dr/dt= -2tr,         r(0)=ro

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Q: 3. Obtain two linearly independent solutions valid near the origin: 3xy" +(2-x)y' - 2y = 0

A: As per the question we are given the following second order ODE : 3xy’’ + (2-x)y’ - 2y = 0 And we…

Q: Find the general solution of y’ + (1/3)y = exy4

A: We have to find the general solution of the differential equation y'+13y=exy4 .

Q: Obtain general solution of y' = y + y^3.

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Q: find the solution satisfying the initial conditions: y''-y=x^2 , y(0)=0 , y'(0)=-1

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Q: Find the general solution to y" – xy' = 0. -

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Q: Is y(x) = C1sin2x + C2cos2x, where C1 and C2 are arbitrary constants, a solution of y” + 4y = 0?

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Q: 19. Show that yı = 1 and y2 = /x are solutions of yy" + (y')² = 0, but that their sum y = y1 + y2 is…

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Q: (a) Solve y" + xy + (2r – 1)y = 0, %3D near z = -1, if y(-1) = 2; y'(-1) = -2.

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Q: 6. Find a general solution to the third order equation y" + y" + 3y – 5y = 0.

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Q: Obtain the family of solutions 1) xydx – (x² +3y² ) dy = 0 2

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Q: Find a general solution of y"- iy'+6y= 0.

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Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: 4. Find for the particular solution of y' = x3 – 2xy when x = 1, y = 2 x2 а у 2e + 2 - ex2 b. y =+…

A: The given differential equation is:y'=x3-2xywhich can be written asdydx+2xy=x3which is a first order…

Q: Show that y = - In x + 3x - 5 is a solution of y" -=0. Use y = - Inx+3x – 5 to find y' and y". y' =O

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Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 2e-2 Y(t) =

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Q: Obtain the particular solution. y' = x exp(y-x²) ; when x = 0 , y = 0.

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Q: Show that y = In (x) is a solution of xy" + y² = 0.

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Q: Obtain the general and particular solution 4. xydx + (x² + y²)dy = 0

A: The given problem is solved below in detail.

Q: Obtain the general solution valid near the origin: 2y'+9ху'-36у 30

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Q: 2 ydx = 3xdy; when x = -2, y = 1 Ans. y = (x/2)3

A: Given: 2ydx=3xdy ; x=-2, y=1   We know that; ∫1ax+bdx=1alnax+b+C

Q: Suppose ay" + by' + cy = 0 with y(0) = d and y'(0) = k has a general solution y = 4e2 3. What are…

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Q: 3. Obtain the general solution of: (x – y)(4x + y) dx + x(5x – y) dy = 0

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Q: -Find the solution of y"+y' + by = 0 by transforming y = x"u|

A: Put y=xαu in the given equation y'=xαu' y"=xαu" Then the equation becomes xαu''+axxαu'+bxαu=0 Now…

Q: b) Give a particular solution for y" – 2y' + y = et - 1+x2

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Q: ) Find the general solution of the DE y = (2+y')x+ (y')².

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Q: Q2. Find general solution of the DE 4y" + 4y" + y' = 0

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Q: Solve y' = 6x, x' = x + y with initial conditions x(0) = 1, y(0) = -2.

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Q: Verify that y = 1/(x+ C) is a solution to y'= -y², where C is some constant. Find the particular…

A: Given that: y=1(x+C)

Q: 2. x (х — 2)у" + 2(х — 1)у' — 2у %3D 0 |

A: Power series solution of the differential equation

Q: Find the particular solution of: y' – 4y = x²e* that satisfies y(0) = 2.

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Q: Yp = Find a particular solution to y" + 5y' + 4y = - 19te³t.

A: Introduction: The differential equation has a particular solution, which is a singular solution of…

Q: a. Find that solution of y' = 2(2x-y) which passes through the point (0, 1).

A: SINCE YOU HAVE ASK MULTIPAL QUESTION, SO WE WILL ANSWRING ONLY FIRST QUESTION.

Q: Find general Solution of y + +y+ 4y = Ct1)e Using method of vanafion.

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Q: 4. Verify that y=cx+e² +1 is a solution of the equation y=y'x+(y')' +1.

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Q: (D³ + 2D² - 5D - 8)y = 0, when x = 0, y = 0, y = 0, y" = 2

A: Given

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.