Linear equation with nonrational coefficients

DSolve[x''[t]+(E^(-t)) x[t]==c,x[t],t]

Note: //TraditionalForm automatically converts output to TraditionalForm.

DSolve[x''[t]+(E^(-t)) x[t]==c,x[t],t]//TraditionalForm

Abel's equation

Here is a solution to an Abel equation of the second kind, returned as the solution to an algebraic equation involving hypergeometric functions.

DSolve[y'[x]==(((x^7) - ((4 x)/25) + y[x])/y)[x],y[x],x]

Nonlinear PDE

DSolve can now generate complete integral solutions to nonlinear PDEs; FullSimplify simplifies the result.

DSolve[((((∂_x) u[x, y]))^2) + ((((∂_y) u[x, y]))^2) == (1/(1 + u[x, y])), u[x, y], {x, y}] // 
      FullSimplify