(3 Points) Solve the IVP. (1 + x² + y² + x²y² )dy = y²dx, y(-1) = 1 O + y = tan-x + 4 O = = cosx + 4. O y - = tan-x+ I 4. %3D O : = = y cotx + JT %3D 4

Q: The lowest point on the graph of y = cos x, 0sxs21, occurs when x=

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Q: Find dy/dx in terms of z and y if cos² (3y) + sin² (3y) = y + 15. I

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Q: EX selve (I+ COSX)y = Sinx (sinx cosx-y) %3D solve EX) 2dX+ (2X-y+3 )dy = 0 %3D

A: We solve the differential equation with help of integrating factor.

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Q: 6. dx dy + cos.

A: Given: dydx=yx+cosy-xx

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Q: dy Find for three only: dx 1) y = In(cos x . Inx²)

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Q: 3. :-3 + x – 5x² + 3x³ + 3x* x² +x- 2 Evaluate -dx 2

A: find integral then evaluate definate integral

Q: cos2ydx + tan y dy = 0 x = 0; y = 9

A: Here we have to solve the given differential equation

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Q: dx

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Q: 3. arcsin (cos A 3

A: Consider  arcsincos5π3

Q: csc² xcotxdx 4. S csc?xc 4-cot?x

A: As per bartleby guidelines we only give first question answers.

Q: dy/dx=y^2 find all sol for the diff equation above thanks

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Q: (Sin ² x - y) dx - tanx dy =o

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Q: Evalutes x sinx dx x²+2x+2

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Q: 5-2x dy if y = cos Find dx %3D 5+ 2x

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Q: L G -S 2 (5² +a²)2 11 t sihat 2a

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Q: 6メ-8) - $(4)= =1 Cos x (8-x9- 15) %3D

A: Since in part 1st given equation has no rational roots so I will do 2nd question

Q: Y= 5-e- COSX by %3D

A: Given: y=5-e6y=cosx( This question is don't have to specify word  find  and how to find the answer)

Q: General Sol. of  y' tanxsin2y= sin2x+sin2y is

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Q: 大 1-cos X P-V= 2

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Q: y = cos³V2x – 1

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Q: check

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Q: t /2 ccosx CT-X sin(x +y)dy dz dx Jr/6 Jo

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Q: Which of the following is correct? dx dx 2 + C 3x 1 Arcsin* + C 2x { A} S = Arcsin: {C} f V4-9x2…

A: Option C is   correct Answer

Q: Find and if dy dx² dy dx = 5 sec 0 and y = 5 tane

A: Given: x=5secθy=5tanθ

Q: s+1 L- s2 +4 cos4t + sin4ta O 1 cos4t + –sin4t b O - 1 cos2t +-sin2t.cO 2 cost+sint dO

A: We first write the given function in expanded form then we will use the propertie of linearty of…

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.