DSolve[x^2(1-x^2)*y'[x]==(x-3x^3-y[x])y[x], y[x], x]

DSolve[y''''[x]-16*y[x]== x^2, y[x],x]

sol=DSolve[y''[x]+3*Sin[y[x]]==0, y,x]

Plot[{y[x]/.sol[[1]]/.{(C[1])-> -1, (C[2])-> 3}, y[x]/.sol[[2]]/.{(C[1])-> -1, (C[2])-> 3}}, {x,-5,5}]

DSolve[(y[x]+x-1)*y'[x]-y[x]+2x+3==0, y[x], x]

eqn=y'''[x] + 3*y''[x]-25*y'[x]+21*y[x];
sol=DSolve[eqn==0, y[x],x]

sol2=DSolve[eqn== x^2, y[x],x]

sol=DSolve[{y''[x]-((1/x)-(3/(16x^2)))*y[x]==0, y[1]==1, y'[1]==4},y[x],x]

DSolve[(t-1)(t+1)*y''[t]+t*y'[t]+(-2-6*t^2)*y[t]==0, y[t],t]

DSolve[y''[x] + (3 Cos[2x] + 5)y[x] == 0, y, x]

Plot3D[MathieuC[5,-(3/2),x]* MathieuS[5,-(3/2),y], {x,-3,3}, {y,-3,3}]

sol=DSolve[{y'[x]^2==1-x^2, y[0]==2}, y, x]

Plot[{y[x]/.sol[[1]],y[x]/.sol[[2]]}, {x,0,1}]