UVxvL0xpYnJhcnkvRnJhbWV3b3Jrcy9NYXBsZS5mcmFtZXdvcmsvVmVyc2lvbnMvMTEvYmluLkFQUExFX1BQQ19PU1g2Ig==

odes:={diff(x(t),t)=-y(t),diff(y(t),t)=x(t)};

PCQvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInhHNiI2I0kidEdGKkYsLCQtSSJ5R0YqRishIiIvLUYlNiRGLkYsRig=

dsolve(odes,[x(t),y(t)]);

PCQvLUkieUc2IjYjSSJ0R0YmLCYqJkkkX0MxR0YmIiIiLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmRidGLEYsKiZJJF9DMkdGJkYsLUkkY29zR0YvRidGLEYsLy1JInhHRiZGJywmKiZGK0YsRjRGLEYsKiZGM0YsRi1GLCEiIg==

sol:=dsolve({op(odes),x(0)=1,y(0)=0},[x(t),y(t)],numeric,output=listprocedure);

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

ax:=rhs(sol[2]);

Zio2I0kidEc2IjYnSSRyZXNHRiVJJWRhdGFHRiVJKXNvbG5wcm9jR0YlSSlvdXRwb2ludEdGJUkleCh0KUdGJTYjSWluQ29weXJpZ2h0fihjKX4yMDAwfmJ5fldhdGVybG9vfk1hcGxlfkluYy5+QWxsfnJpZ2h0c35yZXNlcnZlZC5HRiVGJUMpPkk4X0VudkRTTnVtZXJpY1NhdmVEaWdpdHNHRiVJJ0RpZ2l0c0dGJT5GMSIjOkAlL0ktX0VudkluRnNvbHZlR0YlSSV0cnVlRyUqcHJvdGVjdGVkRz44Jy0mSSZldmFsZkdGODYjRjA2IzkkPkY6LUY9Rj8+OCUtSSVldmFsR0Y4NiMmSTxkc29sdmUvbnVtZXJpYy9kYXRhL21vZHVsZXNHSShfc3lzbGliR0YlNiMiIiQ+OCYtX0ZESSRHZXRHRiU2I1Evc29sbl9wcm9jZWR1cmVGJUAkNC1JJXR5cGVHRjg2JEY6LkkobnVtZXJpY0dGOEMkQC4tSSdtZW1iZXJHRjg2JEZANytRJnN0YXJ0RiUuSSZzdGFydEdGJVEnbWV0aG9kRiUuSSdtZXRob2RHRiVRJWxlZnRGJVEmcmlnaHRGJVEpbGVmdGRhdGFGJVEqcmlnaHRkYXRhRiVRK2VuZ2luZWRhdGFGJUMkQCUtRmhuNiRGQDckRlxvRl9vPjgkLUZONiMtSShjb252ZXJ0R0Y4NiRGQC5JJ3N0cmluZ0dGOD5GXHAtRk5GP0AmLUZXNiRGXHAuSSZhcnJheUdGOE8tRkY2JEZccCIiIjBGXHBRKXByb2NuYW1lRiVPRlxwLUZobjYkRkA3JFElbGFzdEYlUShpbml0aWFsRiVDJEZkcEAkLUZXNiRGXHAuSSVsaXN0R0Y4TyZGXHA2IyIiIy1GaG42JEZANyQuSSVsYXN0R0YlLkkoaW5pdGlhbEdGJUMkRltwRmhxMy1GVzYkRjpJIj1HRjgtRmhuNiQtSSRsaHNHRjg2I0Y6NyRGZnFGZnJDJEAlLUZXNiQtSSRyaHNHRjhGYXNGW3I+RlxwLUZONiMvRmZxNyQiIiEtSSNvcEdGODYjRmdzPkZccC1GTjYjL0ZmcTckRmByRmdzRmhxL0Y6US5zb2xucHJvY2VkdXJlRiVPLUZGNiNGTi9GOlEoc3lzdmFyc0YlTy1GUDYjRl11QCUwOSFJKHVua25vd25HRjhPLS5GY3VGP0MkPjgoLUkocG9pbnR0b0dGODYjJi1GUDYjUTBzb2xuX3Byb2NlZHVyZXNGJUZfck8tLkZqdUY/WiVDJD5GXHAtRk5GYXNGXnJGJVlGJUYlRiVGJQ==

ax(t);

LUkjYXhHNiI2I0kidEdGJA==

ax(1);

JCIzMkV3VVZJLS5hISM9

ay:=rhs(sol[3]);

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

alpha:=<sin(t),ay(t)>;

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIpL1dSNQ==

plot([alpha[1],alpha[2],t=0..4],scaling=constrained);

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

sol2:=dsolve({op(odes),x(0)=1,y(0)=0},[x(t),y(t)],numeric);

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

plots[odeplot](sol2,[x(t),y(t)],t=0..4,scaling=constrained);

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sol2(3);

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