INTRODUCTION TO DIFFERENTIAL EQUATIONS HOMEWORK I-weeks 5,6,7,8 DEPARTMEN T OF MATHEMATICS Lecturer: Doç. Dr. Tahsin ONER Name and Sur name: Student ID: Signature: 1. Verify that the differential equation (5x+ 4y)dr+ (4r - 8y)dy = 0 is exact and find its solu tion curves. 2. Solve the differential equation ry-(1+2)y = ry? by using appropriate substitution. an

Q: Solve the differential equation (D+ + 5D² + 4) y = sin x + cos 2x.

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Q: 3. y = Ci + C2 e- 4x

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Q: 2. Solve the differential equation y" + 3y csc V3x

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Q: For the differential equation given below, variable. d²x dr2 + kx=Acost is the independent variable…

A: Given :d2xdt2+kx=Acost

Q: (D²+4)y= 4csc³2x (by Variation of Parameter

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Q: dy = e2x-3y, using separable variable method. dx Solve the differential equation

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Q: dy 2 +y- 2x + 3 ご

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

Q: y(4) 4х + 2хе %3D

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Q: 2. (4x + 3)ydx + 4y²dx = 0

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Q: y= c, e2t + Cze-+

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Q: (x? + 2ху — 4y?)dx — (x? — 8ху — 4y?)dy %3D 0

A: Given, x2+2xy-4y2dx-x2-8xy-4y2dy=0....(1) Let, y=vx then, dy=vdx+xdv Replacing the above values in…

Q: y= C, e + Cze-2+

A: Formation of the differential equations

Q: * + 6x) dx + ( In x - 2) dy = o 3. (2x y2 + 24) dx + (2x²y+ 2x)dy = 0 2.

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Q: dy Solve the differential equation dx ху+2у-х-2 - ху-Зу+x-3

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Q: Solve the differential equation dy dr 4x - x³ 4+y³ so that the point (0,1) lies on the solution…

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Q: Solve the following differential equation: yde+xdy 1-x²y² +ædr=0. = constant.

A: Given that the differential equation ydx+xdy1-x2y2+x dx=0

Q: ry? V1+ x²

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