In each of 7 through 16, find the general solution of the given differential

Definitions: Chapter​ ​14.4-Double​ i ​ ntegrals​ ​i​ olar​​ orm 1)​​r​ ​​ ​ ​​ ​x​ +y​ 2)​​x​ ​​ ​=​ ​ osθ​ c 3)​y​ ​​ ​=​​ inθs Chapter​ ​14.5-Applications​ ​of​ ​Multiple​ ​Integration 1)​​ f​ ​σ(x,y)is​ ​ ensity​ ​function​ f​ ​​ amina(thin-sheet)​ ​then​​ he​​ ass​​ f​ he​ ​lamina​ ​can​ ​be​ ​given by​ ​​ ​ass​ ​ ​ ∫∫σ(x,y)dA Theorem: Chapter​ ​14.4-​ ​double​ ​Integrals​ ​​ olar​​ orm 1)​​∫∫ f(x,y)dydx = ∫∫ f(r,θ)rdrdθ R R 2)​ Area​ o ​ f​ ​​ ​∫∫ 1 * rdrdθ R 3)​ ​Proof​ ​for​ ​1*r​ ​for​ ​Polar​ ​integrals.​ ​Consider​ ​the​ ​area​ ​of​ ​a​ ​sector: A​ ​=​ ​½​ ​r​ θ dA​ ​=​ ​r​ ​dr​ ​dθ NOTE:​ ​To​ ​decide​ ​rather​ ​to​ ​use​ ​cartesian​ ​or​ ​polar-graph​ ​the​ ​region Chapter​ ​14.7-Triple​ ​Integr