In this worksheet, we will practice identifying and solving separable differential equations.

Q1:

Solve the differential equation ddπ¦π₯+π¦=1.

Q2:

Solve the differential equation ddπ¦π₯=β5π₯π¦ο¨ο¨.

Q3:

Solve the differential equation ddlnπ»π =π π»β1+π π»ο¨ο¨.

Q4:

Solve the differential equation ddsecππ‘=π‘ππποο‘.

Q5:

Find a relation between π¦ and π₯, given that π₯π¦π¦β²=π₯β5ο¨.

Q6:

Solve the following differential equation: ddππ‘=π‘πβ5π+π‘β5ο¨ο¨.

Q7:

Solve the following differential equation: (πβ5)π¦β²=2+π₯οcos.

Q8:

Solve the differential equation π¦+π₯π=0οο.

Q9:

Solve the differential equation ddπ¦π₯=β5π₯βπ¦.

Q10:

Solve the following differential equation by separating it: π₯π¦π₯=(1βπ¦).ddο¨ο ο‘

Q11:

Find a 1-parameter family of solutions for the differential equation π¦π¦=(π¦+1)οο¨, π¦β β1.

Q12:

Find the implicit solution to the following differential equation: sinddcos(π¦)π¦π₯β(π₯)=0.

Q13:

Which of the following is a solution of π₯+π¦π¦β²=0 defined for all β4<π₯<4?

Q14:

Find a relation between π’ and π‘ given that ddπ’π‘=1+π‘π’π‘+π’π‘οͺο¨οͺο¨.

Q15:

Solve the differential equation ddπ§π‘+π=0ο¨οο°ο¨ο.

Q16:

Solve the differential equation ddπ¦π₯+3π₯π¦=6π₯ο¨ο¨.

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