How to solve these equations by Mathematica?

l tried it with Solve,DSolve and NDSolve functions,but all failed.Should l simplify the equations in the papers or use other mathematica functions.Thanks~

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• People here generally like users to post code as Mathematica code instead of images, so they can copy-paste it. It makes it convenient for them and more likely you will get someone to help you. – Michael E2 Feb 3 '15 at 3:09
• An equation is entered using == instead = (Equal instead Set). (This is not enough to solve your problem, btw). – Michael E2 Feb 3 '15 at 3:10

My vnis are the integrals of your vns
eq1 = 1/2 - Integrate[Sin[v1i[a]] Cos[ArcTan[v1i'[a]/v2i'[a]]], {a, 0, t}] == v1i'[t];